After reading @GalacticCowboy's answer it got me thinking, and after a little research I was able to find this.
Natural Gas contains a small amount of moisture (approximately < 5%) and this moisture will freeze in the winter in long exposed piping runs. Some of this moisture ends up in the gas pressure regulator and will freeze the diaphragm inside the pressure regulator causing it to malfunction or close off the gas feed.
Source
Not sure how cold it is where the problem is being experienced, but it is possible for the gas to be restricted by a frozen line.
This might also explain why it works temporarily. The line may not be completely blocked allowing gas to build up in the line beyond the blockage, when the fire place is turned on it burns up the gas in the line and then is starved once the initial build up is depleted.
This could also be caused by some other type of blockage, partially closed valve, improperly installed pipe, or some other type of blockage.