Yes, get rid of the Pertonix. Every vehicle I own runs on breaker points with the exception of the 70s Ford trucks. They're all I drive and points have NEVER let me down in my entire life. GM HEI died on my '72 Monte Carlo a long time ago.
But ya, if you are getting the correct spark and voltage to the dizzy top, either the cap or rotor, or both are bad. Don't go by looks, either. Had the same problem on a '36 Auburn. All parts looked perfect. Couldn't understand it but a new cap fixed the problem.