Floyd Rose system:

say you hit an open E.
now say you pull the tremolo bar all the way up and release. Hit the E again.
now all the way down and release again. Hit the E.

a guitar which has a good and healthy floyd rose bridge will produce the same tone all 3 times.

my guitar (washburn RS-980) will produce three Es which will slightly diverge from one another. Respectively to the example above, the first E will be correct, the second one will have slightly higher pitch and the 3rd one slightly lower. Naturally, i'm guessing after the tremolo use, the bridge does not come back to EXACTLY the original position.

what causes that to happen? how can i fix this?
Might want to lube up the knife edges and see if that helps. You're correct in your assumption - if it's settling too far up or too far down after using it, that's what is throwing your tuning off.
Ibanez RGA121 | ESP LTD H-1000
Axe-FX Standard
Is your nut locking properly? Is your knife edge lubricated? Is it returning to the same position everytime?
nut is 100% ok. just took it apart, not only are the knife edges not lubricated, they're starting to get blunt.

looks like imma have to get a new bridge..
thanks a lot everyone