The engine light comes on to let you know that an 'error' condition has been met and that your ecu has generated some error codes, might be something like "NO OXYGEN SENSOR READING, NO TEMPERATURE READING" etc reaching the ecu.
In your particular case i dont know what error is causing it to come on, but if you read about your engine and the error codes you should be able to receive them from the computer by putting a little wire into the diags plug to short two pins and putting the key in the 'on' position. Just find a manual or something on your engine and find out the exact procedure, if you are lucky enough to know someone with a Tech 1 diag system, they can just plug into your diagnostic port and read the error messages this way.
Maybe these error codes will help you with your engine cutting out troubles.