Why does a Briggs and Stratton 4.5 HP lawn mower engine stop 2 3 seconds after it starts unless you continue to prime it?

it is losing its prime... i have the same problem right now and i have cleaned the carburetor, changed the gas and spark plug and changed the air filter. The only thing that i can think of is that there is something wrong with the priming bulb or the gas cap is hindering the air flow... still trying to repair....