Does the engine rev up OK when it is running, can you check for a blocked exhaust?
Have you done any diagnostic testing or are you just working through the list of usual suspects?
Assuming it is the engine management light which is coming on, you really need to get the fault codes read, then clear the memory. Run/drive the car till the fault occurs again, then read the faults again.
The diagnostics should be able to record live data too, which would be very helpful especially as the car seems to fail at a fairly consistent time.
What model year/engine code (eg Z16SE, X16SZR etc.) do you have? It may be possible to manually read the fault codes, though this is not ideal as you cannot tell which codes are 'present' and which are 'not present'.
fred
April 2011