Have read many posts about how defective (brand-unknown) radios would turn themselves On and kill the chassis battery, (phantom load on chassis battery) but never radio issue like yours. BUT, first thought on yours is radio AUX Power source is COACH, so WHY is CONVERTER dropping below 13.2vdc on shoreline? 2) WHY is radio dropping out? It should stay ON down to 8-10-volt, maybe lower? I would triple check converter and coach batteries and connections? CHECK FOR RELAY CHATTER at the IRD/BIRD (if equipped?) & CHARGE SOLENOID? (As solenoid contacts go bad, they can THUNK, yet NOT connect) Good Luck
There may also be a CUBE RELAY used to select the radio power source with flaky contacts?
(TerryH.) 2000-GS Conquest Limited 6266 Class-C 99-E450SD V10