How's your mixture? As my old 150 Stombergs wore out I had to keep enriching the settings as it was stuttering in the mid-range with them set to what had been the optimum. Eventually the mixture got so rich that I got starting problems both hot and cold, which triggered me to change the carbs. It hasn't missed a beat since.
Having said that, the only actual breakdown I've had was down to the modern MSD multispark ignition module failing at full throttle (my fault I believe as my 'work in progress' header tank had just dumped a load of boiling coolant all over it) -
Phew! Lucky I had those cones on my head when I set off.
My point is that modern electronics can both help and hinder an old car. Perhaps your distributor has a fault that only manifests itself when hot. I'd be inclined to change back to a standard distributor and see if it cures the problem. If it does, you have your answer. Good luck.