When it dies, and you wait an hour, how long do you crank before it will start again? My first step for you would be after it dies, unplug and then plug in the shut off solenoid to see if that is working. If it clacks while plugging it in that's a usually a good sign. They rarely go bad but it is possible.
Where did you get the injection pump from?
If the solenoid clicks, the next step would be to check for air bubbles in the fuel supply. You start to do this by installing nylon hose from the hardware store between the filter and the pump. If you find a steady stream of air bubbles you're sucking air in from somewhere.
You could be ingesting air but it's odd that it would take 15 minutes to do so.
The people at oilburners.net in the 6.9/7.3idi section will know more about your engine then anyone here.