Just curious, how HUGE a change in pitch?
Rich said fat knives/pinched studs and I think everyone else will agree . . .
This can cause as much as a half step sharp on your low E string in the worst case. (This is rare, however)
Just remember though, "100% Perfect Float" is more rare than platinum. Most guitars will still be a touch sharp on pull-up even with nearly perfect knives and studs.
Rich has found that a little Chap-stick on the studs helps with this (though my G string still comes back 4 cents sharp, I can live with that, I just split the differance when I tune, 2 cent flat from dropped and all sounds fine to the ear ;-) ).
Pain in the tucas, isn't it?
Once these things are working as well as they can, they are hard to give up once you get used to "perfect" tuning. :-)
Are the studs locked properly? Sometimes this can fix 50% to 90% of common tuning problems with the Edge.