Sounds like it might be the heater element.
https://www.geapplianceparts.com/store/parts/spec/WE11M10001
The dryer also has some thermal cut-off sensors.
https://www.geapplianceparts.com/store/parts/spec/WE04X31037 and https://www.geapplianceparts.com/store/parts/spec/WE04X30381
Here is what the manual has for troubleshooting your problem, but it has nothing about the dryer turning off after a little while.
[image|3678022]
That makes me think that it could be the temperature cut-off sensor/s (image - 506 and 507) being faulty.
[image|3678025]