How frequently does the trem get used? If you have a relatively new guitar or even an old guitar with springs that haven't been "exercised" they can get stiff and make things difficult to keep in tune...at least that's been my experience with them.
To solve it, I never had to do anything more than flog the hell out of the trem for several minutes, really work it in a "Vai on crack" sort of way and stretch the crap out of the springs over and over again. Periodically, I'll do this with all my guitars if they start to have tuning issues that can't be explained any other way.
Again, this has worked for me every time when I experienced the problem you've described and I found nothing else wrong. That doesn't mean that there isn't something else wrong with yours, but give this a shot, hope it works...looser springs really loosen up the feel of the guitar too, it'll play much nicer after you flog the devil out of it consistently for a while.