if it is causing that much trouble you can pick up some cheap heat trace and put it around the pipe and have it only turn on when the temperatures gets below freezing. That way no matter how much it isn't protected from the outdoor elements with a poor seal it will stay warm. If it is the whole copper pipe You could mount the faucet to the wall itself and replace the copper pipe with pex. the problem with this solution is that the outside faucet is held by the copper pipe and pex is flexible, hence the mounting it directly to the outside wall. But with pex you do not need to worry about it freezing ever since it will expand and contract with the rise and fall of temperature.
