I would like to give my players the option of learning a way to make a spell or magical effect permanent. To this end I've created a homebrew spell, Spell Permanency (quoted below).

Before implementing this spell in game I would like to be aware of the potential ways in which this spell could be unbalancing and or exploitable. I have attempted to address some of the concerns raised by previous editions with limitations in the spell. These limitations may (or may not) be too severe.

Spell Permanency

5th level transmutation

Casting Time: 24 hours/level of spell being made permanent

Range: Touch

Components: V, S, M (diamond worth 1000gp per level of the spell being made permanent, one willingly given attunement slot of the caster or recipient of the permanency spell)

Duration: Permanent

While Spell Permanency is being cast the duration of the spell or magical effect being targeted is extended for the entire casting period. Once the casting has been completed the duration of the targeted spell or magical effect becomes permanent.

This spell can only make the duration of 3 spells, or magical effects, affecting the same creature permanent at any given time. For the avoidance of doubt, no creature can have more than three permanent spells or magical effects active on it at any given time. Any casting of this spell which attempts to make a spell, or magical effect, on a creature permanent beyond this limit fails.

During casting the caster must be in constant contact with the object or creature upon which the target is affecting. In the case of a portal being made permanent the caster must have one hand placed through the portal for the duration.

While casting this spell the caster is unable to gain the benefit of resting, and suffers all of the effects of lack of rest. While the spell is still being cast, levels of exhaustion gained from a lack of rest can be removed from the caster by Greater Restoration. After the casting has finished, these levels of exhaustion can be removed in the normal way.

Spells or magical effects that have been made permanent can have their permanency removed only by the use of the following spells: Wish, Dispel Magic cast at 9th level (dispel magic automatically fails if cast at a lower level), Greater Restoration (which only works if the creature who sacrificed the attunement slot is willing).

A spell or magical effect that has an alternate end condition will still end if that alternate end condition is met. For example a permanent duration polymorph will still end if the creature affected by it is reduced to 0 HP. Similarly a creature under the effect of a permanent invisibility spell will still end if the creature attacks or casts a spell.

If a spell or magical effect that was made permanent has it's permanency removed or ends prematurely the attunement slot used as one of the material components in the casting is regained.

Whether or not the casting of the spell is successful, the creature who gave up the attunement slot suffers three physical stresses which cannot be reduced or avoided in any way. These stresses remain in effect for 10d6 days. For each day the creature spends doing nothing but resting, eating and reading the total recovery time is reduced by 3 days.

1. The creature immediately suffers one level of exhaustion, which is only removed at the end of the period of stress.


2. The creature's Constitution drops to 3, if it isn't 3 or lower already.


3. The creature's speed, for each form of movement, is reduced by 10ft. If this reduction would bring the creature's speed below 0 in any one form of movement, it instead drops to zero.

How balanced/exploitable is this homebrew spell?

Experience from other versions of the game where permanency was gamebreaking is welcome. Both in terms of how this homebrew potentially avoids those pitfalls, but also potential pitfalls it doesn't avoid.

It's shenanigans, all the way down.

Permanency is full of them. In particular, it's almost not possible to balance Permanency completely. As it is, in 5e, high-level wizards (and other casters to a lesser degree) get some entertaining things that they can do to abuse the system for significant permanent beneficial effects, generally restricted to spell level 6+ (the level when you can start socking clones away to achieve immortality). Permanency, in whatever format, is nearly the most perfect form of this.

4th ed, the edition most obsessively tuned to prevent over-time accumulations of this kind, eliminated Permanency entirely. 3rd and 3.5, which were nearly the most open in letting people come up with fascinating new ways to break the system in such ways, still limited the kinds of spells you could make permanent to a specific list, and had it require the investment of permanent resources in the form of exp. 5th ed hasn't added permanency at all, in spite of it being iconic, and in spite of them having a focus on bringing back many of the iconic things that 4th ed dispensed with.

More to the point, 5th ed has the concentration mechanic, which generally limits ongoing spells to one per caster at any given time. Currently, in-game, there is no way for a PC caster to have more than one spell under concentration. There are no races that can do it, there are no feats that can do it, there are no class features that can do it. There's a clear attempt here to make the concentration limitation a big part of balancing spellcasters, and Permanency basically takes that balance and shatters it.

So... so far as I can see, there really is no way to balance this one. You'll either make it nearly unusable, completely balance-breaking, or both. If the designers could have come up with a version that didn't break everything, it seems likely that they would have, and it breaks many of the current balance assumptions. This is something that a few of the very-high-level spells are allowed to do to a degree (Hi, Wish! Hi True Polymorph!) but even there it's done with some pretty stark limitations (...bye, wish.)

Now, if what you want to do is significantly crank up the level of shenanigans available to your wizard, then you could maybe try to design the spell around that. Permanent magic effects could conceivably be balanced against major magical items. The attunement slot cost is a good start there, though it should be specifically on the target, rather than the caster. Still, even that would take quite a lot of work to make non-game-breaking, because "material component, plus days, plus can cast this spell" results in a radically different level of effect than "magic item, attainable at this level". It might work with some sort of a 3rd-ed-esque "list of acceptable spells", curated carefully. Regardless, the version you have there is definitely exploitable.

This is very broken. The most obvious way that it is broken is that players will use it on greater invisibility.

To understand the balance of this effect, we can compare it to the legendary item ring of invisibility. The invisibility from that ring breaks whenever the wearer attacks or casts a spell. We have some discussion at What is the reasoning behind the Ring of Invisibility being Legendary? about why this is game-breaking. This "permanent greater invisibility" effect is much better than the ring of invisibility, and any wizard can create it for three separate characters, for a price of 4000gp, on reaching ninth level.

Players might also use this on haste and fly, and possibly true seeing.

Note that in 3.5e and in Pathfinder, only the standard invisibility spell can be made permanent, and then only on objects (not on creatures). There are, in fact, whole lists of which spells can be made permanent, and any spell not on the list is assumed not to work unless you get DM permission. If you're really trying to port this spell to 5e, at minimum you should do the same amount of diligence by listing the spells it will work with.

You've attempted to balance the spell by adding downtime requirements, but I don't think this will work. The penalties associated with this spell are bad enough that characters will simply refuse to adventure while the penalties are active. What will happen is: the players will say "hey I want to cast permanency, do we have three weeks of downtime?" and the DM will answer "yes you do" or "no you don't". So essentially you could replace all that text with one sentence: "the DM can, if they want, tell you that you don't have enough downtime to cast this spell."

Specific exploits

Simulacrum

With simulacrum, you have a perfectly loyal schmuck who can take all of those negatives for you. They can chill in their permanent Mordenkainen's magnificent mansion being waited on by 100 servants, while you run around with permanent invulnerability.

Wish

Wish can be used to cast spell permanency in 1 Action by duplicating its effects. It will also waive the component cost, which should be minor anyways at the level you can cast wish.

This could be avoided by raising the level of spell permanency to 9th.

Amulet of Health and a warhorse

With some preparation, you can cast the spell yourself. The most debilitating of the three stresses is the reduction in your Constitution score. The rare magic item Amulet of Health sets your Constitution score to 19, which should override the reduction.

Now that you don't die from a stiff breeze, buy yourself a warhorse. You can cruise around at 120' per round as if nothing happened. Better yet, splurge on twelve warhorses - they tend to evaporate at the first sign of fireball.

Delayed blast fireball

Delayed blast fireball could theoretically deal infinite damage. It starts at 12d6 damage and increases by 1d6 every six seconds. After waiting one day, it will deal 14412d6 fire damage for an average of 50,442 fire damage on a failed save. I hope the target has Evasion or fire immunity!

The bead can be moved by making a Dexterity saving throw against your spell save DC. A 17th level rogue can have a +11 to Dexterity saving throws, which rises to +16 standing next to a paladin with 20 Charisma. Throw in the resistance cantrip and a Ring of Protection and you can carry the bead completely safely.

Specific limitations

Concentration

You cannot cast spell permanency on a spell for which you are maintaining concentration. This is because any spell with a casting time longer than 1 Action requires concentration while you are casting it, which will end any other spell you are concentrating on. (Since the duration becomes "permanent", not "Concentration, permanent", I am assuming that any concentration requirement is lifted once spell permanency is completed.)

This limitation is lifted by using wish to duplicate spell permanency.

Balance

The current incarnation is very overpowered, especially for a 5th-level spell. Even as a 9th-level spell, its power would rival wish.

As Ben Barden says in his answer, this spell is nearly impossible to balance. Either you have enough restrictions that no one will use it, or you don't, and everyone will. As new source material comes out, you would need to evaluate each new spell for further exploits. It may instead be easier to create a series of magic items or long-to-infinite duration versions of existing spells, which could each be balanced separately.

Balancing a great effect with avoidable downsides is not balance.

This spell creates a long-term effect. Any downsides that don't last as long as the effect are avoidable. This includes the casting time, the exhaustion, etc; any one of them makes this a "downtime only activity", which is one restriction. Piling more of them on doesn't do anything narratively. So they are, for the most part and balance-wise, fluff.

Which leaves the 1000 gp requirement and the attunement slot as the only long-term costs.

Attunement slots are balanced against (a) getting a magic item, and (b) having a limited number of them.

This spell grants a 4000 gp better-than-legendary-item effect (greater invisibility). So neither attunement nor cost produces balance here.

There are two approaches that can balance this with any hope of success.

The first is to create a bespoke list of effects that can be made permanent. This is what other editions of D&D have done.

Audit each and every spell you add and look for issues.

The second is to first lift the magic item creation rules, and make this spell basically "imbue target with a magic item you create as part of casting it".

Such a magic item ends up being in most ways superior to a traditional one, as it cannot be as easily lost or stolen, not being merely an object. But at least it is the right ballpark.

You'll note that magic item creation rules are also heavily in the DM's hands.

Playtesting is needed

Without the added constraints, this effect is obviously game-breaking. Having to add so many drawbacks to a spell in order to balance your spell is a sign that you're stretching too hard to make this work.

That in itself doesn't necessarily mean this is broken, however. In fact, some of the downsides you've added, particularly the unavoidable stress for 10-60 days, make this seem possibly under-powered. I would recommend against using this in an important or long-running campaign until you've playtested it, which would honestly need one or more whole campaigns to experiment with the effects of the stress.

Quantify how to stay in contact

If you do plan to go forward, I would specify what can break simple contact. Even if you have the caster strapped in like a backpack, I'd argue a strong enough jolt could still cause enough separation to break contact. I suggest looking to Concentration-breaking rules for inspiration.

In any case, this is highly subjective

This might not be a good question for StackExchange, which is intended to be a place where fact- and experience-based answers can be gleaned. Answering your question boils down to speculation, unless someone else here has experience implementing this type of effect in 5th edition; due to its specificity, it seems unlikely.