I would think the OL is indicating that there is too much demand on the AC output of the Inverter. If it was a battery issue, I would expect you to get a low voltage error.
When you are plugged into shore power or using the generator, the transfer switch should allow AC to pass directly through the Inverter so I assume you are not getting an OL error when there is shore power or while the generator is running.
If your coach is similar to mine, the Inverter is only powering the fridge and a couple TV's.
What Inverter do you have?
It could be an Inverter problem.
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