Your getting "vacuum"not "pressure ,right ?..sounds like its letting vacuum build up,only source of that would be the lift or injector pump sucking fuel from the tank,I assume..
Most gas caps do have a pressure & vacuum release built into them..
Here they have a machine to test them during a yearly inspection,they have to pass or you cant get an inspection sticker..
I have no clue if a diesel uses the same gas cap as a gas powered truck would...looking up what part number is listed for your truck and doing some googling will likely show what the specs are ,when it should open to release pressure,and break the vacuum..
I would think the engine would starve for fuel eventually,if no air can get into the tank and let the fuel flow to the lift pump and injector pump...it would be like dipping a straw into a glass of water,putting your finger over the end,and lifting it up--the water cant flow back out until you break the vacuum by lifting your finger off..
I had a puzzling stalling dilema on one of my riding mowers,it would start and run great for about 5 minutes,then stall,and not re-start unless I let it sit,it would just crank over..
After cleaning the gas tank,replacing fuel hoses,and cleaning the carb,with zero change--I finally found the gas cap had a vent on it with a "cap",and a lot of mud was blocking the vent,probably mud dauber wasps...soon as I cleaned that out,it never stalled again..