Improved invis acts *very* oddly sometimes when you change your held item: I had some mobs tracking me that were too low level to see past improved invis. I held a talisman (instead of an artifact) and suddenly, all the mobs attacked me as if they could see me. After fleeing, they couldn't re-initiate, as usual.

Here's a snippet:

You stop using a silver-bound tome.
You hold a warm topaz shard in your hands.
A minotaur slave yells '! Nnoow yoou die!'
A minotaur slave's beating wounds you.
A minotaur slave yells '! Nnoow yoou die!'
You drive a minotaur slave's beating back with your connecting blow.
You parry a minotaur slave's beating.
You parry a minotaur slave's beating.
A minotaur slave has some small but disgusting cuts.

Note that I didn't "fade into existence" in any manner there.

It is specific to certain items, and there really isn't a good way around it.