House battery question

Have you been keeping the house battery electrolyte level above the plates? Any battery, while charging, will need to have fluid levels checked periodically and replenished when needed with distilled water. Batteries are damaged when electrolyte levels are below plates. Our stock converter overcharges the house battery and electrolyte levels drop below plates if I forget to check and add distilled water. Check whether your converter is actually charging the house battery. It should read around 13.6 volts on your voltmeter when fully charged, with no load. I'm surprised that your starting battery stays charged enough to start engine when rig is not driven for months. Starting battery also has parasitic loads on it, plus any battery self-discharges over time. Battery maintenance, including periodic cleaning of terminals is important.