[Wigtail]

Sounds just like a fuel pump problem. Mine has around 58 psi key on. I checked it today. Tricky though since there's no place on the engine fuel rail to check it. Had to check it at the fuel filter. My 5.7 350 chevy was doin the same thing. If it started it would run fine. If it wouldn't, i'd just squirt in a little fuel and away she'd go, till you shut her off. A new fuel pump did the trick. Watch out for those junk pumps on ebay. Been there, done that. Go to carquest and get a lifetime warranty. The whole module and all was less than just the pump anywhere else. Good luck.