It has been run 35 hours in the past four years. My initial guess is that there is an electrical failure in the generator side and the engine is not getting a signal to keep running. Other possibilities are low oil level and sensor is shutting down for that or fuel starvation from partially gummed up fuel line won;t provide sufficient fuel to support the load when the generator once it tries to pick up the load.
I wonder if there are any codes? There is a light on the switch, it should provide an initial code such as 2 blinks followed by 1 which leads to another code which can be found in the manual. This is where real trouble shooting begins after checking out the simple stuff like oil level.