Sounds like an electrical connection problem, which usually occurs on the negative side. That's one of the new fangled ones with PC boards, so it could be one of those, too. The older ones have a their schematic on the inside of the lid of the control box. Perhaps yours does too?
Many of the smaller Onans use Kubota tractor engines to power them. If you can figure out which model you have, engine (not generator) parts are much cheaper from a tractor place than Cummings/Onan.