I bought a 94 Ford L9000 dump truck with an M11 and it would start right up but would lose prime and quit after about 30 seconds. Then it had to crank for about 20 seconds to get fuel and be good for the rest of the day but usually needed a boost. I put a Baldwin filter on made especially for Cummins and it didn't solve the problem. Another guy using the truck said he gave it a little throttle after starting and it kept running. I got a couple new batteries because the old ones would drop under 6 volts when cranking. I put them in and after starting held it at about 1200/1300 RPM. After 30 seconds it had a bobble like it was running out of fuel but caught in a couple seconds and kept running. Then it could idle normally while the air pressure built up. Went out the next day and had the same success. If all I have to do is give it some throttle for 40 seconds to keep it running on start up, I'm a happy camper. Reading online it's not an uncommon problem for Cummins M11 and N14's. Maybe someone else can benefit from my experience.
Sounds like fuel is bleeding back to the tank overnight. Maybe getting some air in the system when that happens.
It's more annoying than a big problem but if giving it a bit of throttle gets it past losing prime it isn't a problem at all. Another truck owner says all it takes is a tiny air leak on an O-ring or something similar to cause it. The engine runs great otherwise and is easy on fuel.