Check your manual, I get the code also if I start driving right away. If I wait 60 seconds before the car moves, I don't get the code. I don't know the technical reason, but it is explained in your manual.
As I recall, you have to drive for a certain time or distance in a straight line for the AH to 'warm up', which doesn't happen while autocrossing. I think that's why you're getting the message so 'late'. I remember a previous post from someone who experienced the same thing while autox'ing. Maybe try a search on 'warming up' or something similar?