Nut grooves!
We had a nice Strat in today with a tuning stability problem, especially on the g and b strings. The guitar had been hard tailed so it was unlikely that the bridge end was the issue, as the tremolo couldn’t move. I loosened the strings, and on further inspection it looked like the nut grooves were not very clean and just didn’t look right. I ran a nut file of the correct size through every nut groove, and found that every groove snagged on the file. I proceeded to clean the grooves and re cut them all to the correct depth. After doing this each string ran freely through the grooves, not snagging or catching. After playing the guitar and finding its tuning to be stable, the guitar was returned to a happy customer.
So if you are having any problems with tuning stability, bring the guitar in as there may just be the same issue with the nut on your guitar.
Roberts Instrument Repairs and Accessories 