i had this problem about 4 months ago. car would start, idle rough and then stop.
ghead the diagnosis from the mechanic was a faulty coolant temp sensor - it was giving the ECU the wrong coolant temp therfore the wrong engine temp when doing a cold start. this caused excess fuel in the engine. might not be an identical problem/solution to yours but hope this helps. the new temp sensor came in at $78 australian. hope this helps