I am using a TV as a monitor for my desktop PC. It will shut off when the PC goes to sleep but will not turn back on when I wake the PC back up.

So shut down the computer rather than using sleep.

What happens if you turn the TV off and back on again after coming out of sleep? Or perhaps the TV changes sources when it no longer gets a signal and you need to reset it to PC (or DVI) as the source when you come out of sleep.

The TV is acting exactly the way its designed to.