if the cel comes on while the engine is running and then you jump it while it's running and doesn't go out then usually a sign of a bad ecu...not always, but most of the time.

try this...start the car. when the cel comes on stall out the car w/o turning off the key. try jumping it at that point. it'll keep the code stored.

everytime you switch off the car the cel clears from the temporary memory. when you turn the key back on but engine off all the diagnostics are seeing what they want to see, but once it's running it'll be an item that only operates once the engine is running.

is this a chipped ecu? there could be something very simple that needs to be corrected.