If it shuts off instantly as if you turned the key off I would look at somethinng electrical. Possibly a coil, or loose ignition wire usually purple. Check the wire at the ignition switch at the terminal marked "ign". Then work your way back.
If you are getting air in the fuel system it is probably a loose fitting on the suction side. If the engine dies that quick and then restarts without cranking, then I dont think it is fuel related. The carb would have to run out of fuel to die, then re-fill the bowl before it would start again. For the carb to run out of fuel the pump would have to stop working so the whole fuel system would be empty. It would not start up right away again.