It's your alternator!!!! If you want to be sure of this just disconect all the wires from it ( insulate the bare wire from touching any thing ) put charger on batt and i bet it runs forever......let me know if this helped.
cam position sensor has failed
what makes my ford thunderbird stall and sometimes die and not start back up
it is crankshaft position sensor.
If it is the 7.3L diesel .I would check the crank sensor.
check the fuel filter, may be clogged.
does it stall/ have lack of power. has it ever overheated? cylinter walls may be warped.
Check for leaks in the intake manifold or a poor fuel pressure situation.
sounds like vapor lock check to make sure gas line isn't touching motor it will cause it to stall or die then once cool start back up
If it stalls at idle or when slowing down, it could be a fuel filter. Or it could be the ignition control module.
Possible fuel filter, fuel pump sock fuel pump, Ignition module are the tops off the top of my head.
Check the gas cap there is a possibility that the vent is clogged and causing a vapor lock.
A bad fuel pump will cause your vehicle to not start or sputter and then stall. A dirty air filter can have the same symptoms.