Gremlins...
Seriously =)
A bad remote control, or power button on the set? Or the IR recevier on the set could be going bad. Try hideing the remote after you turn the set on and see if that keeps it from turning off, if it does replace the batteries and maybe open it up to clean it out. If the IR recevier on the set is picking up something else weird in the room you could turn the set on and cover the window with tin foil or some other obviously IR opaque object to see if it doesn't turn off, after that I'm out of suggestions.