Most likely your coils need to be replaced as they have difficulty holding the valves open as they age. The usual symptom is ignition at the very beginning of a cycle, then nothing until the dryer is shut off and allowed to cool. If this is what you are experiencing, then the coils should do the trick.

You could be dealing with a gas problem, but odds have it that it is the coils (AP2150379) causing the problem. Given the age of your dryer, if they have never been changed, I would start there before looking at other items in the burner assembly.