As stated above, the furnace will continue blowing until the chamber cools down. But it should continue to heat until the thermostat reaches your set temperature (just like in a house). Once it reaches temperature, it shuts the fire off, and continues to blow a bit longer. If it blows constantly and never shuts off, does your thermostat (on your wall), have a furnace and also a furnace-fan setting? If it has a furnace-fan setting, the fan will continue to blow, circulating air with no fire.
Now, if it's not reaching your desired room temperature, it does sound like the gas line is freezing up somewhere.
A few weeks ago I put a comment on these forums suggesting the regulator can freeze up and I basically got blow away with skepticism and basically told I was wrong, that would never happen. But it does. Even some of the posters above just suggested this may be the problem. In very cold weather, the regulator can stop working, thus preventing gas flow. Keeping heat on the regulator will help. The colder it gets, the harder it is to heat a camper. They are not very air tight, not insulated very well, and mostly have single pane windows. It takes the furnace a lot to warm up and start pumping heat through cold ducts under the floor. And those ducts are probably not insulated either.
You might consider supplemental heat, with an electric space heater or ceramic heater. They help a lot! But when outside temperatures are near zero or below, RV furnaces just aren't powerful enough for adequate heat!