My dryer dries really well but never shuts itself off

Dryer: Starts then stops. If an electric dryer starts but then stops before the load is dry, a clogged exhaust vent may have caused the dryer to overheat and trip the thermal fuse. ... A bad drive motor, failed timer or faulty electronic control board can also stop the dryer before the cycle ends.
https://www.searspartsdirect.com/diy/symptom/dryer-repair/1234594/starts-then-stops/dryel09

http://www.appliance-repair-it.com/dryer-runs-for-10-minutes-then-quits-it-will-restart.html

PLEASE do not use this dryer until it is fixed. it may be a saftey hazard. From the sounds of it. Your ignitor is only getting a signal every now and then. Now either is a coupler in there to tell the ignitor when to fire and when not to fire. It seems that it is going out only alloweing the dryer's ignition to come on only when a new cycle is started. That is where i would start... check with an appliance repair shop and find out if it will be something you can do your self or if it is something they have to do....
Now I do STRONGLEY recomend that you have a service technicion come on and service your dryer do to the fact that it is a GAS dryer. if something inside the dryer where to get pinched or broken it could cause a bigger problem....
so please take this advisment under consideration....
Thank you.

When was the last time you got your ducts cleaned? If they r full of lint then the moist air never gets outside and stays in the machine hence the clothes never dry. Might not solve the issue but they need to be done as they r also a fire hazard.

Yes it is . buy new lint filter, you may have to call for repair and cleaning.

you will need to clean the vent tube/internal duct work:

The thermostat tells the dryer to heat until the interior of the dryer reaches a pre-set temperature then the thermostat tells the timer to begin advancing. The timer advances until the interior cools, then the thermostat tells the timer to stop advancing, and tells the dryer to start heating again.

if the vent/duct work is clogged then the dryer may never reach the proper operating temperature, so it doesn't send the signal to the timer and the dryer continues to run indefinitely, even if the clothes are completely dry.

I hope this helps here is a website on how to remove cabinet:

http://www.partselect.com/dryer+amana-open-cabinet+repair.htm

appears that timer is not timing out or shutting off at end of cycle.correct ,the timer itself appears to be the problem.

Getting hot when not started is a great concern.
I have a few ideas why, but this is a fire hazard and I would suggest unplugging and either getting help or replacing.
That said, there here are a few suggestions.
1) if the element is shorted to ground, it will get power to one side of the element and heat though ground. This, again, is serious.
2) if it heats forever and doesn't get warm enough to dry, this is another indication of an element that is not working up to power. Not getting 230 across the entire element and not getting hot enough to dry.
3) Many times when a dryer runs too long, the air flow if blocked by the vent being plugged or some plug withing the dryer itself.

Again, I am very concerned about this problem and suggest you not use it until it is repaired. If you want to check the element, it is fairly easy, but unit will need disassembled.

Mr Boo

IT IS A FIRE HAZZARD. don't use it again, leave it unplugged! there is a problem with the timer or worse. if it is an old dryer get a new one or a used one from a local appliance resale/repair shop. that's where you can get a good deal if you can't afford a brand new one.

If this is a intellidry model, sloped front there is a couple of things you want to check. The problem lies in the electronic control or the sensor bars. You would have to disconnect the wire from the sensor bar and run the dryer. If the dryer runs for about 20 minutes and shuts down or the timer advances then the electronic control is good. The problem lies in the sensor bar, inside the drum. Clean the sensor bar with alcohol. Fab softner can build up on these and give a false reading. To get to the inside of this, you will have to remove the door hinge screws, the door will lift up and off. Then remove the spacers on the other side . The front panel will now pull out and off. From there you will see how to get at the sensors. Catriver

I'm having the same problem with my GE dryer. I think that it may the safety thermostat receaching maximum temperature and shutting the dryer down.
I'm currently researching this problem now.