Well, i had this same issue that stumped me for ages. I would drive the car, all of sudden it would kick off, and sometimes while coasting fire up again.
I thought it was the fuel pump too!
I replaced it, low and behold 3 days later same thing. I took it too a local shop called TAG and they said it was my alternator, i replaced it.
Was not my alternator!
Finally, i took it to another shop where they tested the electrical. Short of it was the computer. The computer was overheating and shutting off the pump. I replaced it and the car has worked flawless since!
So, maybe you can borrow a computer from someone and test it out.
Good luck