As stated, check the fuel cutoff first. I once hit a pothole in NYC that caused it to trip and brought my car to a halt. Luckily, I had a feeling it was that. They can just trip at random, without mini swallowing potholes, and its easy enough to check.

If it is fine, I would then check the inline fuses (unless your SPi has the larger blade-fuse box) on the bulkhead, especially those behind the throttle body. Over time, these tend to give out and contact points slowly melt into the housing, until they no longer make contact with the fuse. I have had this happen twice! I know that the fuel pump inline fuse is in that bunch behind the throttle body to worth a look around.

I do not understand why the battery has anything to do with it. The battery runs the starter. He said the engine quit while it was running. Once an engine is running, you should be able to disconnect the battery hot wire  post and run off the alternator. Stalled out when running and failure to turn over (meaning cranking or firing up?? Which??)  sounds like two different things. Perhaps it is bad  ground wire at block rather than a hot wire problem at the battery.

There is the fuel pump cut off switch that trips unexpectantly. It is located upper right in engine bay. Push it down, once. You should feel it reset. If that doesn't work, do a wire jump from battery to fuel pump. Let us know.

I just reread your post. Are you saying the engine does not turn?

Saw this happen (to an SPI) during one of the runs during MMEMW at Milwaukee a few years ago.  

A few solid whacks with a shoe on the battery terminal connections in the boot effected a cure...

Cheers, Ian

Check the simple things first like the main power cable to the starter it may be loose or corroded and or the battery cables.

Sounds like something electrical/ignition to me.

My Mini with an SPi engine has been running fine all season.  However, on this most recent trip to a friend’s house, it quit unexpectedly when driving uphill.  It didn’t make any terrible noises, it just seemed to have stalled out.  We have it on level ground again and it still won’t turn over.  I was just hoping someone might have some insight before I start tearing into it.  Thanks!