Here are your parts
Model RED4440SQ0

Here is a wiring diagram
https://www.servicematters.com/d...0Sheet%20-%208528190.pdf

You do not have to worry about the heater section (thermostats etc.), they will not shut the motor off which is what I think is happening

Could be a number of things:
1. Motor overheating - The motor has a built in thermal protect/cutoff that opens if the motor overheats but this takes a couple minutes for the motor to cool down for it to reset so from your description of re-starting it is low on the list.

2. Door switch - Could be it is just making, the clothes hit the door, the switch opens and the dryer stops. Bend the switch actuator a little so that it actuates more positively when the door closes. Be careful you do not want to break the actuator.

3. Start relay - Could be weak or have pitted contacts and is dropping out during a cycle. I do not know how you would check this other than replacing it. If bad, sometimes you can hear them buzz but not always.

4. A bad timer contact

5. A loose wire - Low in probability but a possibility