Your inverter has an internal transfer switch, which utilizes shore power input when available and changes to battery/inverter when not. It could be failing, but that won't affect every 20v circuit in the coach, e.g. the air conditioners should still work and the water heater should run in electric mode. They are not powered through the inverter. Check those to be sure the inverter is the problem.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL