I've just clicked this thread to reply. Maybe you've figured it out, but we have to stick together.
From what you say, it may be that cut-off solenoid. The reason I say that is because once a diesel fires up, there's no reason but a 'cut-off' that would impede a warm-start-up. It's this crap they put on to civilize a diesel that just kills us.
Find whatever connections you can to the injector pump housing and clean them up (I've had to just shove them in place and pull them out numerous time to get the connections clean). I'm fairly serious, these bastand 6.9's woill run forever if the damn fuel supply cut-off weren't activated.
So, that's my experience. there's no damn fuel because the cut-off screws up because the conections are corroded.