Will start normally and run for a second or two and then die?

On occasion (perhaps once a month) my Caravan will start normally and run for a second or two and then die. It will do this repeatedly but it continues to die.
If I floor the accelerator and crank for about 5 seconds it eventually starts and will stay running especially if I Rev it up high.
I have changed the battery in the chip key thinking the problem acts like the security feature is shutting off the car when started with a standard (non chip) key but the problem continues.
Problem is random and does not appear to be weather related.
Van runs fine once it is started.
Thanks, Bob