Is the engine stumbling or idling unevenly before it quits?
Check for fuel pressure rise when you just turn the key on. Surely it is as the car starts, but note the number. It will drop some when the car starts/idles when some FP is relieved from the engine's use and low fuel requirement. When you blip the throttle, the lower vacuum pulls less on the internal diaphragm, allowing higher pressure for more power. FP is set (not on stock cars) with the vacuum line off.
Watch for pressure changes as the car dies; which happens first?It there is a vacuum loss, the regulator will richen the fuel mixture. I would also watch for it 'loading up'; too rich. Depending on the local temperature, the time frame you mention might be when the car goes into 'closed loop', bringing all the sensor inputs into the ECM. I still use a vacuum gauge as those indications are as valid today as ever.
I am now, not quite sure why I paid all that dough for an adjustable FP regulator, as my chip is 'cut' for stock FP. Just $$ up in fumes! Lesson learned. I know some tuners like to mess with it, but............
You may have a sensor failing, IF it quits as closed loop happens.
This is an interesting read:
http://www.fuelinjection.com/portinj.html