I don't see the connection with the state of the TV that should/would affect the DVR other than no user input to the DVR after a extended period of time?
Have you tried connecting some other set to that and see if the same thing happens?
How many hours are we talking about?
Abundant OTA television is what makes this country different from all others. Lets keep it this way. If you like Wi-Fi so much, OTA fits right in. After all, it is wireless.