1972 Plymouth Valiant car keeps dieing

I recently am having a problem, when I drive my car for about 30-40mins in the morning, it will start to bog out like its not getting gas then it dies, it starts right back up then does the same thing only quicker, and quicker each time I restart it until it dies immediately after I put it in drive. It's like its not getting gas, but I didn't think it would be driving fine for the first 40 mins. So I thought it might be overheating, replaced the thermostat. Its still doing it. I drained/ refilled the radiator. Still doing it. Next guess is the water pump. Im wondering if a bad water pump could cause this. I don't want to waste my time changing it if its not bad o this couldnt possibly be the problem.