Your symptoms indicate a potentially bad COCH battery.
Use a multimeter and measure across the battery terminals.
You should read around 13.50VDC if the battery is charged, and around 14.5-VDC if it is being charged by your Converter.
If it is only reading around 12.5-VDC then your battery is NOT charged.
With that said, any receptacles you have that operate on your batteries are being powered by your INVERTER, which only powers a couple of receptacles, usually for the TVs and maybe one near the dash for a computer. Be aware that if everything works on shore power and on the generator, except these receptacles that run off your Inverter, then your symptoms again indicate your COACH battery is the problem.
As to your Coach BATTERY SURGE PROTECTOR???? I am not familiar with what you have unless you are talking about what is called a "FUSEABLE LINK" like what is on the wiring of most automobile engine electrical systems, which is there to protect your equipment in case of a "high current" condition.