Well the first thing I would do in your situation is check the transmission fluid level. If the level becomes low, the area where the shift fork sits on the sychronizer will become inadequately lubricated. The problem would probably happen in 6th gear first because of its location in the transmission. Eventually the fork could get "welded" and the car wont move unless the clutch is pushed in because the transmission will be locked up since the gears cannot turn.
That is just my first idea. Other causes could be an improper clutch adjustment, although that is probably more likely to become obvious in lower gears first, since there is less momentum in play. 6th gear is usually easy to pull out of even if the clutch is not even pressed at all.
So basically, I would suggest checking the fluid level, and let us know what you find. The fluid should be just about coming out of the fill hole.