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My 93 Lexus was doing the same thing. Turned out to be a bad EFI fuse (not blown) that would momentarily lose contact, car would shutdwn, then the fuse would cool down and car would crank up. Then it would repeat the process. Replaced the fuse and problem was solved. Replace the fuse regardless if it appears good with your meter.
I had this same problem as well. My EFI fuse wasn't even blown, it was just making poor contact. I cleaned it up and re-installed it and the issue went away. If that fuse is not maknig proper contact, or it's blown, then the ECU will not get power, and the car will shut off. I'd look into the possibility that this is bad on your car before I went and spent lots of money replacing fuel pumps and ECU's. Good luck.