One thing that's not really common but have seen 2 so far was the plastic lower cap that has a heater element gets a pin hole leak and they act similar. But thats 06-07 dt's I forget but I think the max dt's have a different fuel filter assy.
I'd would start by checking the connections and fuse holders in the battery box that feed the ECM and IDM, those were an issue on some of mine. they would act about like what you are saying or just quit and not restart until repaired or doing wiggle test at fuse holder. this was on the 04-08 IC's, haven't had an issue with them yet on the 09 and up's
"I'd would start by checking the connections and fuse holders in the battery box that feed the ECM and IDM," wouldn't the bus throw a code if it was lacking power to the main computers? like ecm relay voltage low, idm relay voltage low or unexpected reset fault?