My genny is gas but I'm having a similar problem. My error code on the switch says the engine stopped without any input from the control or electrical system - IOW, a fuel issue. I disconnected the gas line at the carb, tried to start, and the fuel only shot out maybe 6" to a foot, and not very strong. My rig is 16 years old, so I've got a new fuel pump on order. (I should add it also stops when I'm going down the road, but not sitting still, and my fuel filter is new) The plan is to blow out the lines into the fuel tank, and replace the fuel filter (again) and fuel pump.
Al