I had a similar experience several years ago - fine one minute, wouldn't start the next. The engine would eventually flood. It cost me a couple of flatbed tows. I finally traced the problem to a tiny wire in the distributor that goes from the swivel plate the points and condenser are mounted on to the shell of the distributor. On mine, the wire goes from the condenser screw to the dizzy body. That is where the loose connection was.

Your car is much newer than mine so I can only speculate about what is making starting difficult.

I remember reading that the 65D electronic distributor needs a matching electronic ignition coil with a resistance less than 1 Ohm.  (Standard 12V coil = 3 Oh, Ballast ignition coil = 1 to 2 Ohms).

Rather than repeat hearsay or trust my memory further may I suggest you see the link below to a troubleshooting thread on The Mini Forum.  Info on the 65D distributor starts half way down the page.

//www.theminiforum.co.uk/forums/topic/250724-testing-5965-dm4-distributors-diagnosis-repair/

Hey everyone!

So, my mini wont start from time to time. It will also shut down under driving. I figured the problem is with the ignition. I first changed the easy parts. Distributor cap and rotor. Also plug wires. But still the same problem. When it goes it goes perfectly, but suddenly everything i seems dead in terms of ignition. The car tries to start but no spark. Could it be the coil or the distributor it self? Any advice how i can measure the coil ? Or maybe there is something i didn`t  think about ? 

Engine: 1275 a+
The distributor is a 65d
Coil: Not sure. 

Any tips would be greatly appreciated  
Regards PK