Thank you for your question.
It sounds like you are experiencing faulty gas coil valve assembly. What you are describing is a classic symptom. If the coil valves go bad, or weaken, they will not provide the voltage necessary to open the gas valve on the second or third attempt. The flame sensor then detects no ignition, and the dryer cuts off and delays the heating re-start cycle. These coils are electro-mechanical in nature, and often times the "weakness" is associated with the mechanical aspect of the valve. You can test for continuity on the electrical part of the valve, however the mechanical side cannot be tested.
I would think this is more than likely the cause of your current condition. Below is a link to the part I mentioned above for your specific model. You can order these parts from this same page if you would like to do the repair yourself. Unfortunately on your specific model dryer, the coil valves are built into the gas assembly instead of stand alone parts. Therefore you must replace the entire gas valve assembly in order to replace the coil valves.
I hope this answer helps you in resolving your problem, and thanks again for your question.
gas valve assembly for your Amana model