Phil, when I installed a Pertronix II 9 years ago I researched everything I could and only found coil problems. Most said because they were hot or they used a different coil. I chose to use the stock ballast and never had a problem so far. 

56 Vic, B'Ville 200 MPH Club Member, So Cal.

Now that you have it down to an electrical issue, I would probably replace the Pertronix with a Pertronix 2 since you have the Pertronix 1 which was said to fail if the ignition switch is left in the on position with the engine not running. We all know how electrical devices, when starting to fail can be very sensitive to tempertaure. Also, if the coil is mounted in the horizontal position, I have always purchased epoxy filled coils to eliminate the possibility of the coil core not being fully surrounded by the heat transferring oil, for what it's worth.  What has worked for me with no issues is Pertronix 2 with 1.5 ohm epoxy filled Blaster coil and no resistor. My wild guess would be an issue with the Pertronix unit. However, it's easy enough to substitute another coil then go to that "bad" parking lot and see if that does the trick. These intermittent problem are a real pain - good luck.

64F100 57FAIRLANE500

My coil is mounted on an iron intake with the stock coil bracket.  I could put some material under the bracket to insulate it.  The 1.5 Ohm coil is supposed to work without the resistor.  I'm not sure why the coil would be hot to the touch.  It's definitely a heat problem of some kind as always starts in my garage.

I may have found a problem.  I was using an aftermarket chrome plated ignition coil bracket to mount my coil to the intake manifold.  This turned the coil causing it to contact the intake manifold and the original aluminum valve covers which get quite hot. This may have been transferring heat to the coil.  I relocated the Pertronix coil using the OEM coil bracket with some rubber washers to insulate it. The coil is no longer touching any part of the engine. I am wondering if I should order a new coil as my current coil may be damaged?   It is very hot right now in Central Florida.  I am sure you could cook a roast under my hood. 

If you're concerned about heat saturation of the coil, you might consider relocating it on the firewall.

That is going to be my next move. I have never seen a coil fail this way.  You would think it wouldn't work at all?

I made some bushings to insulate the coil, possibly with sleeve washers and a flat washer of the same material.  Something like this, https://www.mcmaster.com/standard-washers/washers-4/electrical-insulating-sleeve-washers/for-screw-size~5-16/ 
If using a stock bracket, this will require drilling or grinding the hole larger so that the sleeve washer fits inside the hole.  This completely eliminates metal to metal contact between the bracket and intake.

The only reason I did this is because the coil manufacturer recommended not mounting the coil to the engine and I didn't want to drill holes in the firewall or fender.  That coil is now over 10 years old (which is why I'm not sure exactly what I used).


Lawrenceville, GA

I had a problem with my 55 Imperial not starting after it heat soaked.  There's a lot of cast iron in those old hemis!  Coil finally failed completely.  Installed another coil.  Same problem.  
Installed a piece of phenolic board between the coil bracket and intake manifold. That was five or six years ago and that stopped it.  Made one for my 56 Victoria right after I bought it, just in case.
Looks like you've got it figured out.
  Don 

Problem solved.  I emailed Pertronix and asked them about my issue.  Here is their reply.

"I have attached the trouble shooting guide to check the main areas for most common problems 
it could be one of two things, lack of power due to ignition resistance or possibly insufficient ground at the breaker plate of the module."

I checked the ignition resistance and it was within specs.  I opened the distributor and found the small wire that grounds the breaker plate to the side of the distributor was broken. My 1957 distributor has the ball bearing style breaker plate.  It must have been hanging on by a thread.  Glad that's over...   Thanks for the feedback.

In the long list of dumb things I have done playing with cars, this has got to be by far the dumbest.  The following Wednesday my TBird refused to start again. I barely made it home.   I checked everything a dozen times.  Coil OK? Check.   Wires OK? Check.  Timing OK? Check. Carburetor OK? Check.   This left me with the Pertronix Module itself.  I couldn't imagine how a solid state module would start, run, then quit working in the heat of day?  While I was waiting for my new module to arrive, I went over everything again. As I was removing the Pertronix module I noticed the module was very close to the magnetic trigger. Evidently the module had worked loose and I hadn't noticed it.  Pertronix says the gap should be about .040".  Mine was almost touching.  I reset the gap and the engine ran perfectly.  As the engine would heat up the parts would expand and the Igniter would stop pulsing the coil. When it cooled down, the engine would run until next car show.  When it arrives, I'm going to install the Ignitor II and coil and keep the Ignitor I as a backup.  Glad that's over!!