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When it dies and you are trying to restart, are you getting cranking on the engine and no fuel or no cranking either?
If cranking, then proceed here. If no crank, let me know because that is something else. If cranking, then yes, I would lean hard on the fuel pump. If you have it die on you again, turn the key off and back to on and see if you can hear the hum from the pump. If so, then you need a sock for the pump most likely. If you don't, then you will need a pump.
What happens on these models is the sock goes bad and something gets pulled into it and blocks the punk up tube creating suction. Then as the vehicle dies out, the suction goes away and the debris is free. I have seen this so many times on the gas Fords. I wouldn't be surprised if you find a little plastic pellet in the tank. That is from the manufacturing process when the tank was made. I've been replacing socks in a lot of Super Duty trucks because of them in the years of 1999-2005. Yours fits right in that date range.
Otherwise, if you hear no pump at all, then replace the pump.
Now, if you die out and the engine doesn't crank, the issue is in the ground strap most likely. The one from the engine to the frame. The Triton is aluminum and the grand strap corrodes badly. If you get under the truck on the passenger side, look near the starter and you can see the ground strap. Now run it to the engine and where it mounts to the engine, clean it with a wire brush. It should take care of that issue. Very common on these trucks that are in snow areas for that ground strap issue.
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