Im leaning more towards a fuel problem since I have replaced everything in the ignition system. It does have a phenolic spacer under the carb, and its never done this stuff before, so Im going to investigate the fuel system.
Have you checked your dizzy????? HAve you eliminated the possiblilty that the dizzy is too far advanced?
i still think you have a problem with the power geting to the ignition system. the power wire to the system could have carosion some where that heats up and creates increased resistance. this will cause a voltage drop and the igniton isnt geting enough to make a good spark. you need to use a volt meter and look for voltage drops through the system. if the coil has batery voltage when the car wont start then im probly wrong. if it doesnt then you need to back track the power wire till you find the voltage drop.
Being that you said that you replaced the module I would assume that it is an electronic ignition car. I know that you replaced the pickup coil, but thats what it sounds like to me. I have seen several cars do the same thing when the pickup coil would get hot. What you need to do is take an ohm reading across the 2 pickup coil wires when its cold. Then compare it to an ohm reading when it wont start.