I remove all the fabric, and then use diagonal lines to add bracing to the empty frame (which now has minimum wind resistance since the fabric is gone). I look at it like reefing sails, which is to say if one is thinking about it, then that's the time to do it.
It's the same way I don't anchor overnight for purely calm weather; you never know and it sucks dealing with it at 3 a.m.
Additional reasons are as follows:
1) I don't want to be "that guy" whose furling sail, canvas, chairs, or whatever end up causing my boat to come adrift (canvas windage causes extra strain on lines) or fly around and cause damage to another persons boat.
2) Even if my canvas "survived," think of all the extra wear and tear on it from resisting the wind vs. being taken down. (Canvas is not only expensive, but can be a hassle to get - especially if a bunch of storm-damaged canvas in a given area causes the local canvasmakers to have a backlog.) (If you've ever been behind someone towing a boat with the canvas up -- even at 45-50 mph -- you have seen the strain it puts on it.)
3) Hurricanes and storms can be a bit unpredictable and "wobble" a bit. I'd just rather not worry about every little change in trajectory.