Three things I can think of on the Roku that might affect this:
"Settings > Network > Bandwidth saver" -- turn this off
"Settings > Theme (may take a while to load) > Screensaver start time" -- choose "Disable screen saver"
If your Roku has a "Settings > System > Power" menu option, go in there and under "Auto power savings" make sure "After 20 minutes of no interaction" is UNchecked.
But I don't know if the version of their app that YouTube TV has supplied to Roku has it's own "shut down with no activity" feature.
Roku Community Streaming Expert
I am not a Roku employee, only a user like you. Please, no support questions via private message -- post them publicly to the Community where others may benefit as well.
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