We lived thru several hurricanes here in FL, including the big three a few years back and did not remove them. In fact we watched DISH during the storms. My neighbors who have cable, lost their pictures for many hours! If it's installed correctly you won't even have to readjust the pointing of the dish.
Signal strength went up since there were no more trees!
If you want a little more piece of mind you could add struts to the mount (assuming you don't already have them)