I just bought a boat with a 351 windsor. It runs for about 15 to 20 minutes and then shuts down like it is out of gas. When the ignition module cools down or I change it out with a new 0ne, the same thing happens again. How can I correct this problem?

 

We need to know if you are talking about the Dura Spark ignition control box or some other assembly and assuming the motor is carburated.
If you are sure there is no spark with both units then either the distributor pickup is heat sensitive or both boxes are defective.
Also vapor lock might be a problem for fuel.
If the motor is in an enclosed area, be sure there is enough ventilation airflow as well.