I have a 2000 tT444e in a IC chassis. Engine runs great then will start to run rough then stall out sometimes it starts right back up or you might have to crank it then it will start. Most of the time if you shut it down and restart the problem goes away. It will work fine for a week then do it again. Was able to limp it to the shop while it was running rough and checked no codes. found that the fueling pulse width was erratic seem to change every second or two it will go from 0 to 800 to 1700 then back to 800 at 2000 rpm. When the engine is working correctly the pulse width says steady at around 800. I could not find any type of diagnostic test for this problem in the service manual. Any help would be appreciated.
Even though you say you have no DTC's, it sounds like the harness connectors under the valve covers are separating. There was an update kit for this problem which involves installing a plastic wedge clip in the connector, but I no longer have the International part number.
I had the same thing last week with my 02 444, bad connection to the gasket connector under the valve cover. Changed out the under cover wiring harness and valve cover gasket and that fixed the problem