I am sure by now you figured out what had happened, but you didn't mention if you tried plugging your heater into another non GFI circuit. I am surprised no-one caught on that you are plugged into to shore power, but your battery is dead. I had an issue in my Voltage toy hauler, that was plugged into 50 amp, and everything was on, and one day I noticed there was no power AC or DC. I thought the 50 amp had blown a fuse, or some other problem with the 50 AMP, I could not find any problem with that circuit, I tried 30 Amp, and still nothing, when I checked both deep cycle batteries, they were dead. When. I put another 12 volt battery, everything came on. Apparently the batteries went bad, would not take a charge, and when they went to close to 0 volts, every system shut down. With new batteries, everything has been OK since.