illicit: Depends on the initial install - If done correctly, then no, it shouldn't move unless there is a tornado or something.
But lots of installs aren't done very well, sky installs are a common one - screwing the dish to the fascia/barge board instead of somewhere solid, allows flex in the mounting and over time can pull the fascia or barge board off.
like this....
Right, that makes sense. Ours is attached to the chimney, should be pretty solid. It must've moved in the last 2 years as that's when we moved in. I'm assuming the previous owners were using it ok as they had a tv and the install had left the sat dish the only conection in the house.