I think you need to establish weather the power to the ecu is actually failing. Certainly sounds like it isn't to me. You sure it isn't just because the engine is cold it isn't running to its full potential?

You could always log a fault code by pulling air flow meter or something to bring the warning light on, plug it back in, then restart the engine. If warning light is still on, then there was power to he ecu, as this fault would have been wiped if power to the ecu was lost.