The copper in the holding coil retains the most amps of the 2 coils. It gets hot and over time it will fail. Feel it. It gets warm opens and dies. Replace those 2 coils When the gas valve assembly is energized the flame sensor
mounted outside the burner chamber detects the heat from the ignitor. When the heat is very intense then the sensor shuts down the ignitor
and that frees up the power so that the coils can be fully energised and open the gas gates. The gas comes out and hits the red hot igniter and you have ignition. It stays on for maybe 2 or 3 minutes or until the control thermostat is satisfied and shuts down power to the gas valve assembly. So...
If your gas dryer has a good flame sensor and a good igniter AND the dryer will work some and quit, replace these:
Gas operator coils
The coils get hot and quit on these machines when they get a little age on them. It is aggrevating because it is a hard to diagnose thing. But well worth the 20 bucks.