I would pull the inverter. Run it on the test bench. If you can get a schematic you may be able to find out what is wrong and repair it. Providing you have some equipment. To hire someone to repair it probably would cost as much as a new one.
If initially a battery was bad in the RV like freezing, shorted plates etc. it could very well pull too much load on the inverter and destroy the output transistor. Transistors are cheap. That would be just a guess but if just an ouput transistor you could probably repair it for a couple of dollars.
