Engine cuts out, restarts ok

[egallion]

My engine starts fine, then abruptly cuts out. When I hit the starter it starts right back up. On a cold start this happens several times before I get stable running, then it will run for 5 minutes or so before cutting out again. This will keep happening as long as i run the motor.
My electric fuel pump will not prime the carb if I have let air into the lines, such as when I replaced the primary fuel filter to try to fix this, thinking I had bad gas or water in it. I use a priming bulb temporarily to remove the air so I get fuel flow. From other posts it appears that this is normal, and I should install a priming bulb. Is it possible that the pump is not supplying enough fuel? Any Ideas on the abrupt cut-out, restart cycle?