Diesel fuel grows algae, and there are fuel treatments (here in the US) that prevent it. A typical situation is that there is a screen in the vehicle fuel tank, which gets coated with a mucky layer of algae, or that there is an amount of algae and/or other debris in the fuel tank that get's suck against the fuel outlet(screen) during driving. Then, once the vehicle is shut off, and there's no more suction being applied, all the debris or algae fall away. The engine can be restarted, and driven, and then at a certain amount of driving time, the process repeats. It's not uncommon, and gasoline powered vehicles can have the same situation. When I purchased my Coupe in April '92, the seller was getting rid of it because of this issue, and because none of the shops he'd taken it to (in the San Francisco Bay Area) could fix it. The car would run for 30min, die and not restart. Get towed to a repair shop. Sit there waiting to be worked on, and then restart and run fine, as if nothing had happened. I found the screen in the electric fuel pump intake pipe was packed with a 1/2"/13mm thick plug of grit from the fuel tank. It was so packed in that I had to dig it out with a screw driver blade, and then blast the fitting out with compressed air. I've never had a problem since.
Knowing that your campervan has a repeating history, if I were working on it, I'd look to see if there was a pre-filter screen in the fuel tank, and I'd check the fuel tank for debris/rust/water in the bottom of the tank. Depending on what I found, I would move forward through the fuel system, checking for pour fuel flow, and blowing through fuel hoses and pipes in both directions with compressed air (after removing them from whatever they were connected to). I would continue with the "confirm excellent fuel flow" diagnostics, until I had excellent flow right up to the mechanical injection pump AND from the injection pump, returning to the fuel tank. If there's vent in the fuel tank, and/or in the fuel cap, I would also confirm that hose had excellent flow.
It's not rocket science.