I would bet that it is the ECU. You can get screwed by a stealership to the tune of about $1300, or find a remanufactured one for between $200 to $500 depending upon where you go. (I recently found one at O'Reilly auto for $215) The part # should be MB159963 for a DOHC motor.
The problem is, Mitsubishi used substandard capacitors in their ECU's. Over time, the Caps. will start to leak their electolyte. This will cause them to have varying voltages that will wreak havoc on your ECU. It will cause it to shutoff, like you are describing, idle poorly, etc.
If enough of this stuff leaks out, it can fry the whole board because the electrolyte is caustic.
Here is a
GOOGLE search for Mitsubishi ECU. You may want to call around to some local autoparts stores as well. Give them the p# I listed and they should be able to get one for you.
EDIT: The ECU is located behind the radio in the center console. On each side of the console you will see two plastic caps, under those caps are screws. Undo the screws and you will be able to remove the carpet pieces from both sides of the console. There are 2 bolts on the driver side and one bolt on the passenger side that hold the ECU in place.(10mm socket will remove them)