I had the same problem with my Midget for YEARS!!! My Midget was my first car and all through HS it would breakdown sporadically, cool off and then keep going. My dad and I tried everything trying to find the problem. We scrapped the SUs for a weber, ditched the lucas dizzy for a Mallory Dual point, we went through the whole car and couldn't find what was causing the problem. Finally we replaced the fuel pump and figured that had fixed it but shortly thereafter, I parked the car. Then just this last summer, after about 6-7 years, I pulled my Midget out of storage. Same problem. I thought I had it licked because I even took out the "new" fuel pump and replaced it with an ultra-reliable after market unit. Things were fine until I was stranded on the interstate at dusk. I rolled the car backwards on the sholder against on-coming traffic to an on-ramp I had just passed, got it down the on-ramp aways, parked it, and lifted the bonnet in total desperation. There was only one TINY thing that led me to finding the solution and it had never happened until that night. When the car started stalling, the tach started jumping all over the place. I had checked and rechecked the points a thousand times, every time the car had ever done that to me before so I really didn't think that was the problem so, even though the coil was brand-spanking new, I felt some force telling me to check it. I touched it and it was smoking-hot!! Luckily there was a very reliable auto-parts store just down from where I was on the ramp. With nothing else to go on, I pulled the coil and walked over to have them test it for me. After a ten-minute walk, the coil was still so hot you couldn't hardly touch it. The guy tested the coil, and said that it was OK, but then he asked me a question that changed my life. He asked "What kind of ballast resistor are you using?" "Ballast resistor?", I replied. I know that me AND my friends, never knowing what a ballast resistor did, had scrapped the ballast resistors any time we had ever put a new coil in to anything. He then proceeded to tell me that if you don't have the proper ballast resistor, you run to much voltage to your coil AND YOUR POINTS, they get to hot, you burn your points, car cuts out. All those times in high-school when it would quit, the first thing I would do was pull the dizzy cap and check the points. That would air it out just enough to cool things down and when I put it all together again, it would start up and run awhile until they got to hot again. So the guy at the auto parts store was going to sell me an external ballast resistor for the chrome coil I had, but being that I was stuck in the dark on the side of the road, I had him sell me a new coil with a built in ballast resistor so that I could just hook it up and drive away. Funny, I have never had a problem with the ignition system or my points since. Lesson learned. If you look at the points and they are white and powdery like they have been running way to hot, that may be your problem. Good luck.