Update: I have followed a lot of the recommendations in response to my initial post and from friends in the local Model A club:
1. Changed the coil: A friend in the local Model A club mentioned that he had a similar problem and when the engine compartment heated up the coil internal expanded and caused a break in one of the internal coils. This didn't fix my problem, but when I took the old coil off, it started leaking. So, replacing it was a good thing.
2. Set the timing and points gap: Multiple people recommended setting the timing and the points gap. I did these, but they did not fix my loss of power issue. These were easy to do, so a good step in trying to fix my problem.
3. Rebuild the carb: I had a Zenith carb on the truck and pulled it off and replaced it will a Tillotson that I had rebuilt. This fixed my problem to some extent, but not completely. I rebuilt the Zenith and put it back on. However, when I reinstalled the Zenith carb, I also installed a phenolic spacer between the carb and the intake manifold. This spacer reduces the heat transfer from the intake manifold to the carb. These prevented the loss of power issue, but I started having severe overheating issues on hot days.
4. Had my radiator re-cored: To fix the overheating issue, I had my radiator re-cored. This fixed the issue. Although the flow tubes in the old core weren't in terrible shape, there was some blockage the restricted the flow to some extent - even after back-flushing the radiator.
So, the loss of power issue was really an overheating issue. The truck never fully overheated (coolant boiling) because when the engine got hot, it cause the gas in the carb to boil first. This resulted in the engine losing power because it wasn't getting gas. When I switched out the Zenith for a Tillotson, the Tillotson was better at dissipating the heat from the engine and prevented the gas from boiling to some extent (the Tillotson is made from pot metal and the Zenith is cast iron). When I put in the phenolic spacer between the intake manifold and the carb, it prevented the gas in the carb from boiling and allowed the engine to continue to run (no loss of power). However, this allowed the engine to continue to heat up and the coolant would boil - severe overheating. Having the radiator re-cored (and back flushing the cooling channels on the engine) has now fixed the overheating issue. I also removed the license plate from in front of the radiator to the bumper and use a mix of Watterwetter and Sierra antifreeze as coolant. Watterwetter provides a better heat transfer from the engine to the coolant and the antifreeze has a higher boiling temperature than straight water.