Had an issue with mine with 6 gallon fill-up, though mine wasn't dying for that reason.
Could drive 1/4 mile to the station, put 6 gallons of gas in it, go home and let it sit stinking of gas all week and put more 6 gallons of gas in it again.
Broken tank, 10" crack about half tank level.
My dying problem was at at a plug, broken wire to the plug for the coil.
Agree with Fyer58, yours sounds pressure related.
Replaced my pump and it ran 35PSI, as it should be.
Shut it down after it warmed up, and about 30 minutes later it actually went up to 41PSI.
Probably engine heat getting to the fuel rail, started dropping after that.
There is the off chance it could be a fuel pick-up rotted off, ethanol is not kind to older fuel systems, but I doubt it.
Could still be a rot issue on the pressure side of the pump where enough weight of gas against the leak will let it run.
Not enough and it won't.
I know it's a bitch, but I'd start with the pump And the sending unit.
And a thorough inspection of the tank while it's out, check the vents and remove the skid pan.