Is this electronic ignition or points?
Burned points from leaving the key on, engine not running, points closed?
Have you checked point gap?
Is your condenser well grounded?
Have you done voltage drop testing to see if you have any undesired high resistance? What you describe sounds like a primary side issue...
If you have electronic ignition, pull your coil wire and hold it close to a good ground. Grab a Weller-style soldering gun and bring the soldering gun housing close to the ignition module and trigger the gun. Coil should fire at 60 Hz from the induced field - meaning module is OK. Check for damaged wires on dist. pickup assembly (rotation of breaker plate by vacuum advance can cause intermittent drop-out.)
A few ideas to start with. From your description, I would put money on the burned points if this is a mechanical distributor.