In the 70's and 80's their primary mode of failure was intermittently dropping out when they got hot causing stalls, etc. It would start with a quick buck as the ignition was lost while driving and then come right back almost before you knew it happened. It would take a long time before one would die and stay dead long enough for the techs then to figure it out which is how that reputation developed as you can imagine the frustration felt by owners and techs alike.
The symptom here sounds like one of the other failure modes when the Ignition Start circuit in the box isn't working and then when the switch is let back to Run the box works and there's just enough inertia left to carry the engine through. This can be ignition switch or wiring related though since both wires on the two-wire connector must be energized during cranking (box grounds through the distributor btw).