Your dryer has the classic symptoms of overheating due to the duct being blocked. when was the last time you cleaned it out? Or the dryer itself? With an item that gets as much use as it sounds as yours does (you plus a tenant) lint can accumulate rapidly.

The machine does not get a lot of use.

Yesterday I took off the back pannel and front of the dryer.
In the back I vacuumed up the dust which was not back. I cleaned up the motor area and all around the back side. Looking into the back vent seemed fine.

In the front there was dust but not much which was cleaned up. I cleaned inside burner barrel and around ignigter area.

The front screen by the door opening loads up everytime but gets cleared before each use and is unblocked for use.

David

I'm not positive what "duct" could be clogged. There was not much dust to start with and not enough anywhere to clog air.
I looked at the drawings for the dryer and there is an "air duct" under the lint catch. That was clear to begin with but had fuzz on the sides which I cleaned the other day. The machine still stops heating after starting with heat.

Did you clean the duct that exhausts the air from your dryer to the exterior of the home?

The duct work from the outside of the dryer has been disconnected so there is nothing connected to the back of the dryer.

I looked in there the other day and there's nothing in there up to the turn to the blower. It was clean in there. Although the house has apartments. It one person upstairs and me. I mostly hang my clothes up because I like the way they come out. It has not seen a lot of use over the years. I never cleaned it until this problem but everything was open. The most buildup was below the lint catcher on the sides but clear. It's now very clean and the problem the same. Initially there is heat but it drops out. That's why I've been holding off on doing any readings. I'm also not 100% positive what my unit is. It has the numbers I listed above on it but they are not reognized by the Frididaire site.
I found one place that said my 131066300 was a FDG336LBS0. I found the drawing for that and it seems like my unit except for the drawing of the control pannel. The start button and timer matches but mine has a heat control on the left face of the pannel not shown in the drawing.

David

Have you checked the dryer venting in the house? It will go from the dryer to the outside. The heat then no heat is typical of an obstruction between the dryer and the outside. If the dryer can not move enough air, it overheats and shuts the flame off. Obviously you have cleaned/checked the inside of the dryer, so check the vent to the outside.

The vent ductwork from the outside of the drier going outside has been disconnected. The back of the dryer dumps air into the cellar. There is nothing to obstruct the air at the back of the dryer.

I looked into the back of the vent and it was clean in there and I could see all the way back to the curve going to the blower. It's very open, clear and clean.

As I mentioned above, there was a buildup of lint in the vent below the lint catcher on the walls but there was plenty of room for air. That has all been cleaned up and the behavior is the same - starts out with heat but the heat drops out later. I think all passageways are clear. They have been vacuumed.

The first poster mentioned that the heat dropping out was typical of a clogged vent. I've checked all over for a possible clog and cannot see that any place is clogged.

DO NOT run a GAS dryer if it is NOT vented to the outdoors! This is very dangerous. A GAS dryer MUST BE VENTED TO THE OUTDOORS. You are putting CARBON MONOXIDE into the cellar, it can migrate into the living space above.

From what I have read in other places, I would think it is your igniter. It clicks and lights the first time when you start the dryer but then after the burner cycles off it fails to light the rest of the time. I would check that out with a tech or through one of the repair forums on the web.
You might even call a servicer in your area and they might tell you what it is so you could get the part and do the repair yourself.?