I agree, I would clean the entire fuel system. Drain the tank, new fuel lines, new fuel filter, clean the air filter element and install a new plug. Process of elimination. I'm sue it will run fine after that. New idea, remove the gas cap and try to see if it stays running without it. It it runs, the vent hole in the cap is blocked....easy fix. If it still shuts down without the gas cap, then do fuel system cleaning.