Maybe the fuel pump is marginal where it gets fuel to the carb for starting but not enough to keep it running. Not real likely since I would expect it to run for more than a few seconds before crapping out. Anyway to be sure you could unhook the hose and crank it while filling a jug of some kind. I had a similar problem with a truck where the arm on the pump finally wore enough where it didn't get enough action to pump enough to keep it running. poped in a small electric pump and walah.
