Has the power steering pump fan been replaced? Spin it by hand, it should turn smooth, if it is notchy its time for a new one. Make sure the power steering pump works it is a high load item. I am not sure if that is your problem but it may be. Also the power steering pump is covered by an extended warranty by MINI you may want to check and see if yours is one of the ones covered.
The only other thing I can think of is a short some were. Check along the length of the battery cable to see if maybe chafing has caused the insulation to be worn through.
Let us know what you find.