Hello and thank you for the opportunity to help you.
The most likely issue is one of your gas coils is bad. They can work normally for the first 10 or 15 minutes and then fail once they heat up. I replace a lot of these on gas dryers for the exact same complaint. If it starts to heat, that rules out a lot of things, including your ignitor, fuses, radiant sensor, etc. The part number for the coil kit is 279834. Very cheap and easy repair.