The circuit uses the fact that the amplitude of the pulses from the inductive pickups increase with speed. The flywheel has raised timing strips where the leading edge and the trailing edge determine the two timing angles, one for start and one for normal running.
If the amplitude of the pulses is sufficient to trigger the ignition circuit then there will be a spark assuming that the charging coils have built up sufficient charge in the high voltage capacitor.
I have not investigated the failure mode that causes the starting problem, I suspect that it could be that the threshold on the trigger circuit has drifted to a point where the amplitude of the pulses during cranking is insufficient to trigger the ignition. The fact that heating the module often allows it to start the engine suggests that one of the components is on the edge of its tolerance and the application of some heat just allows it to come back into spec. This is more likely to be a semiconductor rather than a capacitor. It could even be the required gate current of the main SCRs.
Once the engine is running, the self-heating within the module coupled with the increased amplitude of the trigger pulses means that it keeps operating reliably. If there was a problem with the main high voltage capacitor then you would experience problems at all engine speeds and it is likely to be worse at higher RPM.
They key message is to start your engine on one module only from time to time. This way you will detect and dormant starting issues that will be hidden until the second module fails. I suspect there are many engines with at least one faulty module and the owner is unaware.
I've attached the schematic for the trigger circuit if you are interested.
