Ok so not a 12 volt issue no inverter, Check Circuit breakers,.
now one thing about a front mounted TV in a Motor home and there are 3 suspects here
There is an interlock,. it's a CHASSIS not a house device (even though the TV is otherwise a house device)
Ignitiobn on TV off it cuts off power to the TV. ACCESSORY position MAY do that. (or not)
The interlock is a simple relay and usually in the outlet assembly.
SUspect list:L
Bad relay
Ignition not in OFF or LOCKED position
Short on Chassis 12 volt system activating the interlock system.