Originally Posted by Lt Dan
Your problem is not with the GFCI. It sounds like you have low power on the inverter, a circuit breaker on the inverter is tripped, or the inverter is off. Have you checked the condition of your house batteries?
I don't think it's low DC input voltage but I think you're right to question the inverter.
Inverters and generators are "separately derived services" in Code-speak, and those services have neutral and ground *bonded*. With shore power, the RV panel is a "sub-panel" and the ground and neutral are NOT bonded at the RV. Transfer switches and inverter AC pass-through switches are supposed to automatically handle this change of bonding. It sounds like this isn't happening and the GFCI is responding accordingly.
There is also a possibility that there is a ground fault with the inverter itself; electronic things can and do fail, sometimes in unexpected ways.