At first I thought it could be a thermostat because it would sometimes fail to start up after a load as if it was too hot.
A thermostat just cycles the heating element on and off, it would not kill the dryer.
A thermo fuse would kill the dryer, but it would not reset itself.
The motor overload that is built into the motor would kill the dryer and then reset itself after it cooled down.
Have you taken it apart and looked for lint build up around the motor? The motor maybe over heating if it's covered in lint.
If you can catch it when it quits you could also take it apart and see if the motor is hot and ohm out the motor overload to see if it's open.