It sounds more like a fuel problem, but the best thing is to test, not guess!
There is a drain plug on the bottom of the carb. If you'll locate the plug, and have a wrench ready, run it until the problem occurs. Then quickly pull the plug and see if you get fuel flow. There should be a sustained flow. If the flow slows to a drip, there is a restriction somewhere. The inlet fitting to the carb or the needle/seat could be clogged. Also make sure the fuel line is routed away from the exhaust manifold, could be boiling the gas in the line.
If the fuel system checks out, check out the ignition system. Again, best to catch it in the act, be ready to check for spark when it quits running. Take a look at the points and the distributor in general. Be sure the points are correctly set, the wire from the points to the coil is tight and not shorting to ground, the distributor shaft bushings are not worn, and the advance weights are free. Worn bushings are a common problem, points cannot be set if the bushings are worn. Electronic conversion kits are more forgiving of worn distributor bushings (hint, hint!) It could be the coil, but that's not real common.