Thank you for the suggestion!  I removed the cap and reinstalled it to make sure that it was absolutely tight and the stalling stopped.   The stalling began after I filled the car with gas, so perhaps I didn't have the cap on tight afterwards and wasn't creating a complete vacuum.

I had one that stalled because of a vacuum leak when one of the 90-degree elbows had cracks in it. Replaced it with some silicone hose on each end and that raised my idle and stopped the stalling.

Later it would stall while driving steadily and would only restart after waiting a bit.That turned out to be silt in the fuel tank clogging the pickup sock and which eventually took out the in-tank fuel pump. The fuel pump sock would get the build up on it and it woud require that I sit with the key in the off position for a while to allow the silt to fall off and then I could restart it until such time that the silt built back up on it and it would stall again. Keeping the tank more than half full would be must less of a problem. Took a while (and one fuel pump) to figure out it was silt. shining a flashlight in the tank after going for a drive revealed very cloudy gas in there. When I drained the tank and took it out ans swished it around a bunch with fresh gas, replaced the fuel pump and pickup sock for a second time, I never had the problem again.

Under the air cleaner there will be 7 buss fuses. Pick out the brown with gray stripe wires, inspect them, the fuse holder and the fuse. Touch them, don't just look at them. Make sure the silver caps of the buss fuse is solid, make sure the inside connectors are clean. A light sanding of the contact points and the ends of the fuse. Assemble everything again. If that doesn't work and the mini still stalls, tape the two connectors together without the fuse. The mini should not stall. At this point you will need to replace the fuse holder. 

Thank you for your response.  Would you mind explaining further your suggestion of checking the brown/grey wires?  Also, which fuse?

Thanks again.

JG

When you say you don't believe that you don't have a vacuum leak, have you checked the 7 elbows connection points?

Check the 2 brown/ grey wires and fuse. That's what the problem I ran into.

Next time this happens try removing the gas cap slowly and see if pressure releases/suction. Ive had cars before do similiar things and it ended up being a pinched fuel vent or the check valve had an issue.

My 1995 Rover Mini Cooper SPI is stalling when stopping at lights after it is warm.  It usually will not start again until it sits for several minutes. 

It does not appear to be burning rich and I don't believe that it has a vacuum leak.  The plugs and plug wires are new, but the coil and distributor are original.  It has a new fuel filter.  RPMs at idle, when warm, is about 750.

Any advice is appreciated.

John