I am no TV repair man but i had a TV that acted in a similar way and it was (or so i was told) a dry joint,as the TV warms up the the board expands and if there is a crack in the solder it can pull apart and break the circuit,mine was fixed with nothing more than a soldering iron though i was told it was not always 100% effective and I may need a part replacing if the problem returned
hope this helps
pete, July 2012