Teleport capable monsters being able to teleport away when stunned, blinded or confused is a defense mechanism of theirs. It makes these monsters special to fight in their own way and requires the player to adjust their strategy to suit.
I would not like to see this removed from the game.

I don't think it adds any strategy at all for stunning (other instances [i.e. blindness/confusion] are fine). The only way NOT to stun creatures when you are a Thief or Beastfighter is not to melee them because it's a class power - you don't have a choice like, say, the acid blood corruption (which you can theoretically remove) or the phial of Caladriel (which you could not throw), etc. You're forced into stunning if you use melee, which is usually already the most dangerous way to engage such monsters (I guess exception is like fairy dragon/unicorns, but they are quite a bit rarer than your guaranteed balors). So basically, you pepper them with missiles, run/TP around level like bloody idiot tracking down balor, or close levers to bring him back [except he will just disappear again] - I don't see why the already-safest way to engage them has to be the ONLY non-tedious/realistic way to engage them on Beastfighter/Thief. Even stunned, balors would be no joke in melee compared to taking them on with missiles (literally zero risk way).

(addendum: do missile criticals stun on Thiefs? That would suck some pretty hard, they'd be totally screwed.)

Bringing this back up because I was reminded of it by the Wiki's article on Andor Drakon and Thieves/Beastfighters. I think it's a huge problem and really needs fixing as it takes the class powers from "cool" to "absolutely infuriating".

It's the same for mindcrafters and confusion. I guess that should stay as it is, since confusion is quite a bit different from stunning, but still, it's extremely annoying. Both for confused and stunned monsters.

Well the difference is that a mindcrafter can choose not to stun things - a Thief/Beastfighter cannot outside of using Magic/Missiles instead (i.e. a huge divergence from how they're meant to be played). Mindcrafters have very little trouble with these monsters because you don't need to confuse them to take them out [also you get corrupted if you do so].

Are the PC's teleportation powers disabled while stunned?

I regularly confuse corrupting monsters as a mindcrafter, the impact is negligible.
Though I agree that I can just choose to not use it against teleporting monsters because of the very mechanism you described.
I guess this RFE should only target the two specific class powers for thieves and bfs instead of stunning in its entirety.
In that case you have my vote.

That would be the idea, but I'm not sure if such fine-tuned granularity is possible. There's very few cases where stunning comes into effect outside of that [might just be stun ray, actually?], so I don't think it's a big deal to encompass all these things [after all, if you have Stun Ray...well, you probably don't need it to deal with balors / et al. Even if it's from a wand].

I do not know and or know if anyone else knows [I imagine it's a very rare situation to be in...]. It would seem doubtful that the PC teleports randomly while stunned, though [assuming they have +TPitis].

In my case typically wands of stunning are used and only situationally early on against some nasty monsters I might not survive facing in melee.
Stunning is otherwise a near-useless spell since monsters shrug it off with startling regularity so I just ditch it past early game.

Yeah, it's only useful against Mino Mages - I imagine balors would shrug it way too much to make it effective. That's what I don't see a problem with a blanket ban on NPCs randomly TP'ing while stunned [they're too stunned to TP!].

How about making the stunning class powers toggleable?

Well, it seems like a much more complicated solution to the problem, imo. [Though what do I know about how complicated this is, true]

I believe I have introduced a clever special case into the code that should satisfy everyone.