I didn't hook up the main ground from the engine, that cost me 2 coils!

I think (hope) it is associated with using a "cheap" coil. But I will consider and check all the things mentioned. The car started as a very early bare shell (61 or 62). Engine is a A+ 1275. The 123 distributo was added about 6 years ago and has been working very well.

My Mini has a ballasted ignition and whatever coil was on it when I bought it. I added a 123 several years ago (according to the instructiions) and it still runs fine. The red wire supplies 12V to operate the unit, and the black wire is the coil  neg. feed. The current specs indicate the coil primary must have not less than 1.0 ohms rresistance.

//www.123ignition.nl/id/52.html

I had the same problem.  I went to check the distributor cap and a piece broke off in my hand.  The center point had melted and burned a hole in the rotor.  I changed both and had the same issue, changed the coil and no more problems.  I do periodically check the wires have good connections.  On another note, thanks for the used head and transmission, the rebuild came out a treat and I have been driving my mini everyday since, even after the 12" snowstorm!

Yes, some Minis did use a ballast resistor; hence, mur's question.

I had a similar problem after installing a CSI solid state distributor.  After installing the distributor, while adjusting the timing the car started missing, backfiring and eventually dying.  I noticed the dizzy was quite warm and the coil was getting hot.  After checking the installation and verifying the coil resistance was correct for the dizzy I tried again, engine idled fine until the dizzy and coil became hot. After hours and days fretting and thinking my dizzy was dodgy I installed a noise suppression condenser at the positive side of the coil. Bingo started up and has run without a hiccup. 

You didn't mention if the 123 dizzy was a new installation or what year your car is.  I don't know if any mini ignitions used a ballast resistor, but if your car had one and you bypassed it you could possible get a hot coil and may burn it out. 

My car is a '68 Cooper with a generator, solid state voltage regulator, solid state Fuel pump, CSI dizzy and now a noise suppression condenser. 

What is the actual voltage going to the coil and the 123 when the engine is running?

I run a 123 dizzy in multiple cars and generally run the bosch blue coil and haven't had a coil failure yet. Well, except for the ones I've dropped and broken the post on. But even then, I just jb welded it back in place becuase the internal wire was still in place.

Any ideas? It is a 1275 with a 123 distributor. After a relatively short time, the car starts to miss and backfire. I try a lot of things like reseating all the wires and even change plugs. But changing the coil clears it up.