There's two possibilities that are immediately obvious.
The first is that the pressure inside the house is slightly lower than the pressure outside the house before you light the fireplace. This would cause air to flow down the chimney into the house which would keep push the flame into the house instead of up the chimney. This would be easily testable if you could get a free-swinging door. If you opened it inward slightly, it would swing open as air rushed into the house to equalize the pressure. Since the door doesn't swing freely, it might be possible to feel the effect by opening the door slightly and feeling for a breeze coming into the house through the opening. If you get something like a sheet of paper and hold it, it would blow into the house (note -- since the house is warmer than the outside, if the pressure were exactly equal inside and out, one would expect the breeze to move outward -- pulling the paper towards the door -- because the temperature gradient would cause the air to flow outward).
The second, related, possibility is that your house is really well sealed up and so the air moving up the chimney creates a low pressure zone in the house, pulling the flame back in. For the chimney to work correctly, there has to be some airflow. The flame will create some air moving up the chimney which will create a suction within the room/house. If your house is really well sealed, there's no air to replace the air being sucked up and out. When this happens, the pressure will equalize by pulling air down the chimney and pushing the flame into the house.
You could always crack a window in the room to get enough replacement air for the flame to stay within the fireplace. This will cool the air in the house down slightly, which may seem to be the opposite of what you want. But fireplaces actually primarily warm the room/people through radiation and not through heating the air. This is why campfires outdoors can still warm you up even though it's very cold.
Aside from possibly burning the mantle outside the fireplace, a poorly circulating fireplace can be dangerous. The combustion of methane (natural gas) may not be complete and could result in carbon monoxide products. If you do not have sufficient airflow to pull those products up the chimney and out of the house, they could build up within the house itself. Since carbon monoxide is lighter than air, it could build up on the upper floors of the house. Hopefully you have a carbon monoxide detector, but I would be very cautious about running your fireplace without proper air circulation.