Craig, I have a separate battery hooked to the generator. I also have a BATTARY TENDER JR hooked up full time. The bays in the bus were cut out long ago and reinstalled with Marine plywood and painted with several coats of oil base paint to help seal the wood. The generator is mounted to a slide for service (didn't want to cut a larger hole in the floor but did cut a hole for hot exhaust air and exhaust pipe). The ground straps in the generator are good but I don't have one going from the slide to the bus frame.
Do you have to reprime it to restart it? Running for awhile then shutting off sounds like it could be the fuel filter. If you have not ever replaced it I would recommend doing it. I takes very little to stop it up. Mine is an HDKAK so it is a little different.