My inverter usually works fine, but now and again it turns itself off and then can only be turned on with shore power or generator. It will remain on then after you turn the generator or shore power off.
Sounds like possibly your coach battery may be going below the cutoff limit for the inverter which causes it to shut down. The inverter is not used when on shore power or the generator. The converter is used to charge the battery.
I'd check your coach battery and pay close attention to the battery voltage first. Could also be caused by a loose connection or corroded battery terminals. How old are the coach batteries?