The problem appears to be on the 12 volt DC side of the electrical system.
Here are some failure points.
1. 12 volt auto reset breaker is old and starting to fail.
2. Converter is failing and battery is toast, so it doesn't take over the load.
3. Battery is toast and the converter can not keep up to the load of attempting to charge and run the RV 12 volts systems, too.
I'd start with a known good 12 volt battery and no shore power connection. If there are still outages then the autoreset breaker may be the failure point.