3406e shuts down while driving

First things that popped into my mind would be a fuel shut off solenoid, fuel pump issue or something in the fuel tank blocking the fuel pick up, shine a flash light into the fuel tank and look for a foreign object like a rag or contamination. Did anyone pull a fuel sample, check the fuel filters?

 

It should not fall to zero right after the key is turned off. Either a faulty check valve (yes I have had them bad right out of the box) or they didn't replace the o-rings on the check valve. There is also a valve in transfer pump. Or a weak o-ring on an injector letting pressure seep off. But this would cause other symptoms.

 

There is a couple more power wires and ground wires inside the harness that can break. I had that issue. It was the switched power wire that goes go the fuse panel. They also ran two grounds directly to the battery from the ecm bypassing the cab harness. Mine did it for 2-3 years and wouldnt show any codes or anything. When the switched wire would lose contact it was just like turning the key off.

 

I had the same problem about 9 years ago on my than kw with 3406 e. Kw dealers change ecm wireing bunch a sensors i have been towed 4 times and all this for nothing. It was bad silinoid in the breaker box it was overheatting. Change all of them they only 24 dollars a piece

 

The fuel pressure dropping off immediately should affect you going doen the road. Mine drops off slowly after shutting the truck off. I dont even think cat has a fuel solenoid valve. Tge check valve is above the filter head on the side of the engine. 1" 1/4 wrench to loosen it I think? The only time I ever had an issue with it was after the truck sat for 3 months. It would lose its prime as soon as you shut it off. I replaced the valve but it still did it. I had to crack that fitting loose and sometimes fill the secondary filter and the truck would fire up and run perfectly. That fun went on for two weeks and then mysteriously cured itself. I think my threats about sending the POS to Mexico finally got through to the ecm

 

Behind the left hand dash panel theres a main relay. IIRC it supplies power to the dash. Its buried in there. I changed mine when i was chasing the same problem you had. I think it was 35 bucks and a but if a pain to change. You can check the panel for water issues but i think that is overblown. Pete's are inside the cab not like kw where they are half in and half out. Pretty easy to check it in any event. BTW if you have good insurance that relay is live all the time so thats a good place for a fire to start lol