Gas fireplace flame keeps dying?

I have a gas fireplace - if I turn it on, the flame dies in a few minutes. However, if I leave the glass door to the fireplace open (so that air gets in), then the flame does not die. It seems like no oxygen is available in the fireplace to burn. What can I do to fix it?

Public Comments

may want to check the gas pressure or if there is a fresh air vent in the front that needs to be opened.
the glass door should be open, it needs air to burn-you shoul have a mesh screen to close rather than the glass...unless there is a different kind, that is what i know--do you have an owner's manual??
is it the one that turns off by it self and than restarts again , my are a vent less model and you do not shut the doors with the doors open , mine run fine ,, if you have not used it in a while leave doors open to burn any dust or build up off , if it is a vented gas model , were the gas come out might need to be replaced Ron
if you cut it off and look at the tip of the line where the pilot lites, there is a small hole that need's cleaning by sticking a small wire, etc. through it to unclog it. This will let your flame and oxygen mix correctly. A flashlight will help you find it.
Some of the other answers about leaving the door open for adequate oxygen are on target. In addition to this, I have a ventless gas log that was almost brand new that would go out after being lit for a short time. I called the repair man and he came out and "bled" the air out of the gas line. He explained that after they install a gas log it is important to get all of the air out of the gas line feed, or it would cause the problem described above. What he did to bleed the air out was simply hold the pilot light lighting knob down, like he was trying to light the pilot light, but did not light the flame. He did this for a few minutes and it forced all of the air out of the gas line. Haven't had any problems since.
The gas fireplace burns the gas, not oxygen. You may need to check your gas level or call a technition