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The problem is the coils I'm sorry to say. Whether the coils test ok or not, the reason they stop working is that the resistance changes once they warm up and have been opening the valve for awhile. That is why the igniter turns back on but the valve won't open. If you had a bad flame sensor or a bad thermostat, the igniter wouldn't glow. You just need to order and replace the gas coils and you'll be back in business. It's probably the most common way for a gas dryer to fail and the parts are really cheap. Below is a link to the kit which is about $15.
CLICK HERE for coils
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Hello again. I'm just following up because I haven't heard back from you and I see this question is still open. Is there anything else I can help you with?