Has the truck wiring been messed with?
If it's easily repeatable, there should be a red wire hanging off the fuel pump relay. Run 12v to that, and see if it dies under the same conditions.
The fuel pump relay has a redundant oil pressure switch, so it SHOULD run even if the relay is bad. But always possible the switch is bad too.
Sounds more like something is overloading a circuit and tripping a breaker, but I only know of the breakers on the fuse panel. Can't recall what all they feed power to.
The fuel pump circuit is pretty well isolated from others, my suspicion is that you are losing ECM and/or ignition power when this happens, and thus why it dies.