Just as ramsale said, try using a "lubricant" on the slot. I used to use a little bit of chapstick, or caramex (chapstick in a little yellow can), or guitar grease which is what i have now.
If the tuning keeps going sharp (higher than G), then it is the string binding on the nut. Like your playing for a while and all of a sudden it's too high after a bend.
If it is going below a G (flat), then it could be the string (unless this always happens, even on new sets). I had an LP copy that i banged the machinehead (tuner) on a table hard, and it kept going out of tune after that. I whacked the G tuner on mine. That seems to be the tuner that takes the most abuse on 3x3 style headstocks. C'mon, be honest, did you whack that tuner? :smile:
Did you just increase the gauge of strings you use? ie .009's to .010's or higher?
Ramsale covered it very well. Try the least expensive fix first.
Dana