I have a 2005 mini conv. that has 40,000 miles on it. Four times in the past 2 months it hasn't started again after running. It doesn't matter if its a short trip or a long one its just random. Have brought it in for service twice and they say they can't duplicate the problem. If I let it sit for about 45 minutes (found this out the first time after waiting for roadside assistance to tow it in) it will start again. All lights go on, car just won't turnover. Any one else have this issue/ solution for an automatic mini. Lots of the posts are for manual transmission.
Thanks!

 

could be a defective ignition switch