Two famous problems
TFI module
Ignition switch
Both can cause same problems you have. I have to assume a new TFI went in with the "replaced" distributor. The Ign switch can cause you to loose the IGN circut intermittently due to internal wear in the switch, they were also known for catching on fire too
My 88 2.3 Coupe just died while in line for a sticker, replaced the TFI cap rotor and wires (one fell apart when checking plugs) Even though the plugs seemed dry enough, if fired right up again and runs just fine now.
Of course the Dist cap was COMPLETELY stuck on. Had to pull the dist, bust off the cap. Ended up drilling out the old screws after breaking the rest off without any turning from the section threaded into the dist. Made a mess of the dist, but the new cap screwed down good enough to go.
Man what a PITA for a lousy $150 winter beater that my Bro is driving!!