There is a real good chance that the problem is the wire to the pick-up coil for the timing of the spark.
With that design every time the vacuum advance moves the two wires to the pick-up coil get flexed. They are thin solid wires, and somewhere after 60K miles they loose there reliability. They could go any time after that. When they go bad they become intermittent. If it has over 120K miles, it might have been done once before at 60K.
Take the rotor off and very gently one at a time pull on each of the two wires going to the pick-up coil. If one of them is bad it will come off in your hand.
Mark where the rotor is pointing and pull the distributor and look for slop in the bearings. If there is too much play it is time to replace the distributor.
If the distributor does not have too much slop in the bearings, to fix it purchase the new coil, dissemble, replace, and reassemble, but be sure to keep the metal that the old coil was in. Sometimes the clearance between the old metal tabs on the distributor and the metal tabs on the new coil is not close enough to provide good signal, and you will have to use the new coil with the old metal the old coil was in. You could put the rotor, cap, and coil on the distributor while it is out of the engine and rig some spark-plugs with grounds and spin the distributor by turning the bottom by hand while you have it connected to a 12 volt battery to bench test it.
The first time I had one of those go bad my car was about fifty miles from home. One of the wires to the pick-up coil came completely off with the slightest movement. I pulled the distributor and took it home and replaced the coil. Took it back and installed it and it would not run. Took it home and bench tested it and still no spark. I still had the old coil and the old metal the coil was in. Put the new coil in the old metal and bench tested it and wolla let there be spark. Took it back to the car and put it in and it fired right up. Total distance traveled to fix it 200 miles.
I had two other cars with GM HEI ignition fail the same way after that.
Believe it or not, on one of them I was able to scrape the insulation off the stub of wire from the coil and use a soldering pencil to tin the wire, then did the same with the wire that broke off, then joined them with a slight dab of solder. That held until I could replace it.
Another solution is to just buy a re-manufactured distributor, however, re-manufactured parts are often assembled by the lowest cost unskilled labor the over sea company can find, and are known for having many problems.