If it starts it isn't likely air in injection lines, normally won't start at all or will start but run horrible. Does it stumble as it dies or just shut off? It will have a low oil pressure kill and an over heat kill. The low oil pressure kill _may_ have an automatic 'ignore' for several seconds after start then will be put into the circuit. It's designed to stop fuel flow if oil pressure drops and of course until the engine runs for a couple of seconds there isn't pressure so they ignore that sensor.. When they fail (or your engine fails to build enough oil pressure) then it will start, then shut down.. Usually should allow restart almost right away though