I had a bad wire in the engine wiring harness on our 97 Neon. It is the harness that runs from the PCM, around in front to the injectors, - and around the back of the engine and down, to the cam position sensor, the crank position sensor (CPS), the alternator, the oil pressure sensor -- and to both of the O2 sensors. It could be one of the wires for the heater in the O2 sensor is shorting to ground (or to another wire in the harness). That same voltage is needed for the CPS (crankshaft position sensor). That wiring harness was badly melted on mine, and I finally replaced 12 of the wires in it. (Took it off the car to do this). Since then I have also had the wire to the O2 sensor short out due to rubbing against the body in one spot; but that was easy to fix.
While its messy to work under the cars in this area, it may be what is causing your engine to die.
Be careful with the wiring harness! While you can buy a new one from a Dodge dealer, they are about $800. !!
Maybe if enough of us go into auto parts places and -repeatedly- ask to buy an engine wiring harness, the aftermarket folks will begin to make them - for a lot less than $800. I make it point to ask each time I go into an auto parts place where they dont already know me.
Good Luck....