It's hard to say without any further info. In the worst case scenario, you'll need to replace the tuning head for that string, but the problem could also be the nut:
I once had a guitar whose strings would bind in the nut, thus going out of tune once I had done some stringbending or used the tremolo. Another, more experienced guitarist who tried it out at a point, detuned it, took a pencil and "drew" graphite into the string slots. This did make it better since the string slot was now lubricated by the graphite from the pencil, but it only lasted a while. He recommended me to change the nut to a better one, but I got rid of the guitar instead. =)
If the problem is the nut, you could get a "roller nut" (with roller bearings in it) or a locking nut (not the Floyd type, but one with an individual quick-lock for each string).
If it's the tuning head that's bad, lubricating the nut is not going to help (rather make it worse).
I've been assuming that you have a fixed bridge on your guitar. If you have a vintage style tremolo on it, I suggest you stop using it altogether or get a guitar that has a decent double-locking system on it (Floyd Rose).
*EDIT: DCLXVI beat me to it. =)