I've never seen a schematic of a Pertronix--trade secret, I assume--but I think it's basically a power transistor switched by a Hall Effect sensor, and likely some timing circuitry to produce the consistent spark (which gives the somewhat improved performance). If so, it's a 'roll of the dice:' if the engine stops with the transistor forward biased and the key left in 'run' you will likely fry the transistor; if not, it might endure an overnight event. Everything I've heard about them is that, if they fail, it's permanent; i.e. they work or don't. Later Pertronix, the 'II' and 'III' have protective circuitry and other improvements, but last I checked they are only available for negative ground. Note if you leave a points-based system in the same state you would overheat and possibly damage the coil.
I'd first double-check:
- distributor rotor: I have had one fail and there were some crappy ones going around a few years ago
- distributor cap: aftermarket are suspect--even 'Bosch'--and if the carbon plug terminal is worn or broken you could get your symptoms
- secondary wiring: you are not supposed to use stranded copper core wiring with Pertronix (supposedly, the EMI from them can damage the unit). However, I have run two Healeys with Pertronixes and stranded core for many thousands of miles; my guess is because I use resistor plug caps and resistor plugs I have been spared a fried unit. On an episode of 'Roadkill Garage,' the hosts went through several electronic ignition systems--including a Pertronix distributor--a couple alternators and a couple coils before they surmised their copper core secondary wires likely committed the crime
- the ground switch in the boot: In the 'OFF' position it cuts the circuit to the battery but also grounds the coil ground terminal (a primitive 'anti-theft' device). Check for a closed circuit at the ground coil primary next time your car won't start ('SW' or '+' or '-' depending on car's polarity). There should be two wires on it, figure out which is the one to the switch--it's usually white/black--and disconnect it.