I do not know what condition those 2 connectors are in. I will try to look at it in the morning as well as unplug those sensors. Also someone I don't remember who said a possible ignition switch. Do you think that is possible?More than likely you are having an electrical problem.
What is condition of the WIF and fuel heater wires and connectors at the FFM.
Look for missing insulation where they enter the FFM.
Try unplugging them, will run fine and not affect operation.
The PCM can turn off stuff if there is a short, it has solid state circuit breakers.
It will automatically reset, but I would not let it go on doing this for long.
As a test - unplug the BARO, IAT, MAP, and ECT sensors and see if it still dies.