A/C fan shuts off on its own

Welcome back. Your description sounds like the blower motor itself is heating up and shutting off. There is a thermal limiter inside the motor that acts as a fuse. To test if it's the motor or something else you will need a simple test light. The motor is next to the resistor you changed. There is a two wire connection that feeds the blower motor. Take the test light and connect it to those two wires. Let the fan run until it shuts down. The light should stay on while the fan is on. When the fan stops, if the light stays on, the blower motor is the problem. If the light goes out then there is a power issue to the fan. If the light goes out the next thing to test would be the fan relay. They can get hot and stop working as well. The easiest way to test those is to replace them. That is in the relay box under the hood. See the second image.