That's what it sounds like, but the anti-drain back valve is located up on the fuel rail, just before the line of injectors. You are thinking of the roll over valves that are on top of the tank. I have never seen any valves on the gas line itself near the top of the tank.
But for the long run, if its losing its prime, then that's the sign of a weak pump. or a clogged or semi clogged pick-up tube on the pump in the tank. Even if the valve was bad, it should start with 2-3 cycles of the key if the pump was performing as it should.