If there is a screw holding the 'handle' onto the end of each tuner shaft, try tightening them just enough to make the tuner feel solid again. Make it 'snug' [u]not[/u] really tight!

Something else you should try:

Pluck one of the strings that goes out of tune, and then press on the string at the headstock, between the tuner and the nut. The note should rise, and then settle back to proper pitch. If it stays high, the string is being pinched in the slot in the nut.

You can solve this by changing to a lighter gauge string set, or you can get a guitar tech to adjust the slots for you.