I have a 04 mini S and when I accelerate hard the power cuts off and the car will only rev but not drive. It only happens when I try and push it. I'll turn the car off and back on and it turns on a drives like normal. The CEL comes on but it will turn back off after a few times of turning the car off and on (within a few days)

 

need to get that code checked, your going into limp mode

 

Sounds like you're going into limp mode as suggested above. Regardless, you more than likely have a code stored in the system even with the CEL not illuminated. You'll want to get a good code reader or can try swinging by an Autozone to see if theirs can read it. Sometimes generic readers wont work though, but it's an alternative from buying a scan tool yourself.