When did this start happening, was there any other symptoms before this condition presented itself?
A couple of things you can check would be to see if the fuel pump relay and ASD (Auto Shut Down) relays are operating. I'll include a picture of the Power Distribution Center with the relay id. The ASD relay should cycle (turn on) with the ignition switch (it powers the PCM). The fuel pump relay should cycle on for a few seconds then turn off with the key in the "on" position. When you crank the engine over and it starts, the fuel pump relay "should" turn back on once the engine catches. If it doesn't, it could be the computer turning the fuel request off (signal from the anti theft system) or no signal from the cam/crank sensor - you would need a DVOM or a scope to check the sensors out and a scan tool to check for fuel request. If the relay turns on when the engine starts then turns off after it dies, then you would need to put a fuel pressure gauge on it and see what the pressure does when the car dies. If the pressure drops off before the engine dies, it could be a fuel pump or a clogged filter. Further diagnosis would be necessary with a voltmeter to check power and ground to the pump. You could pull the filter and see if it's clogged.
You can cycle the ignition switch ON - OFF - ON - OFF - ON within 5 seconds. Then count the number of times the malfunction indicator (check engine) lamp on the instrument panel flashes on and off. The number of flashes represents the DTC (code). There is a slight pause between the flashes representing the first and second digits of the code. Longer pauses separate individual trouble codes. Depending on the software level of the PCM, it may output codes via the transmission position indicator (if it is a digital position indicator) on the dash.
If you don't have access to a high pressure fuel pressure gauge or a DVOM, send her to a repair shop. A code reader from a parts store won't tell you if the engine is trying to run and then shuts off, of if the engine is being shut off by the computer.
I did a check and couldn't find any service bulletins for the symptom you described from Chrysler
Let us know what you find out, I have access to the repair info here at work....