Most RV's do not have a feature that charges the starting battery when rig is connected to shore power.Those that do, have a device called a "BIRD" that connects the converter charger to the starting battery and trickle charges it while rig is plugged into shore power. Our 2004 Tioga had no such device. I installed a "Trik-L-Start" device that connects the house battery to the starting battery, stealing some charging current from the house battery and trickle charging the starting battery when rig is connected to shore power
Installation of Trik-L-Start on our rig was not "easy" as it required running a long heavy guage wire from house battery to the starting battery along the frame and up under a wheel well to the starting battery with a 15amp circuit breaker near the battery.