It's possible the cap or rotor or both are mi-matched to your distributor.
The tip of the rotor needs to be near a high-tension terminal when the points open and spark occurs.
If you do not have the exact, correct cap and rotor for your distributor and spark occurs when the rotor is on between high tension terminals you are not going to get a reliable spark out of the cap.
Also, are you using the original breaker points setup or an aftermarket EI?
If you put the incorrect EI module in a distributor that's otherwise "correct" the same thing can happen... spark occurring when the rotor tip and a high-tension terminal are not lined up.
I have a "distributor machine" and a variety of caps I've cut a viewport in with a hole saw and can visually check where the rotor is when spark occurs. You want it to be at the leading edge of the high tension terminals, it will travel to the middle and eventually to the trailing edge as distributor seed is increased and the centrifugal advance operates.