Hi all,
I've just registered and spotted this thread. I think that this is due to the A/C turning itself off to protect to pump in freezing (or close to) conditions.
My current Audi A4 has started doing this now that we are well into winter. The first time it did it I checked on the audi forum
http://www.audiworld.com and the reason above was given, it's probably the same for the MINI.
Permanently leaving the climate control in economy (that is temperature control without the AC pump) helps to alleviate this when it is around freezing.
Cheers
Martin.