If it only gives a hard start after sitting for awhile, then it would seem the problem is something other than the Injector Pump.
From my understanding if IP was bad it just would not start.
It would seem you should check, diesel Filters, lift pump, and also the strainer in the tank.
It would seem from what you mention it is getting air in the line somehow when left sitting.
Also check all the lines to see if they could be sucking air.
Finally may sound obvious, but are they keeping the tank full, or is it a situation where they are only putting bare mimimum of diesel in tank when running it.
Hope this helps