Usually the problem is the Chromecast screensaver and the fix is in this thread
If the TV is actually turning off, that’s weirder. Do you still have a Chromecast signal in the TV when this happens? Sounds like a TV issue to me, some powersaving setting?
What model Chromecast are you using and what is the firmware version? Do you have the model with the TV remote, Ultra, Original, or Built-in TV version? You can find information about firmware in the Google Home app → Device → Settings menu → bottom of the screen.