Why does the dryer stop after the pushbutton start switch is released

"Most likely cause is the motor relay. Unplug the machine. Use a multimeter to check continuity across the motor relay on the two pink/black wires. If the circuit is open then the relay is bad. This can also be caused by a poor connection or corrosion/oxidation on the contacts. Pull the connectors off and rough up the male connectors with some fine sandpaper or steel wool.

If the relay checks okay then most likely the control is the problem."