But a general thought might be that the coach batteries are dead as well as the geenrator not getting power to the converter and that providing Dc to keep it running.
I believe the coach battery disconnect will be closed to get the genset to crank. The DC power comes from the chassis alternator when the RV engine runs, allowing the genset to start and run. When the RV engine stops, there is no longer DC for it and it stops.
I would suspect several things?
One is bad coach batteries that won't hold a charge but more likely a problem with the wiring from the generator to the converter and on to charge those batteries. Bad batteries after being stored is common on RV as well as corrosion on things like battery cables.
Possible the breaker directly on the generator but I feel less likely than corrosion.
Engine runs, there is DC power to generato as green line. but no DC from genset to converter on to batteries to maintain DC. When engine stops, DC is not comming from coach batteries nor engine as the mode solenoid opens.
Maybe as simple as corroded batterycable at some point between generator and converter but more likely at the coach batteries where there is a lot from battery fumes?
By no DC out, I mean it may be coming out of the converter but not getting to the battery!