Fred, it is hard to tell. Loss of power could be a bad power supply, it could possibly be heat safety shut offs on other components or maybe even somehow something gets shifted and disconnects due to loose or corroded pins.
CAUTION FIRST: There is a LOT of power in these electrical components of TVs. Be very careful when you're poking around. You can easily injure yourself and possibly even kill yourself.
If you want to check that the power supply is the problem, check its output voltages and look for odd fluctuations during operation, especially around the time that the TV shuts down. You can also try to check the voltages right after shut off...maybe another component is shutting down but the power supply is still operating properly?
Hope this helps and be safe! Let us know what you find.