If it is caused by a loose gas cap, the car needs to see several 'driving cycles' with the cap tight before it will reset the light. I'm not sure how the car defines a 'cycle' but I'm sure it's more than a simple start and restart. It likely involves getting car up to speed, the engine warmed up, and a set number of miles. However, based on your experience with driving modes, I'm guessing it's not as simple as a gas cap.