When hurricane Marty hit La Paz, BCS, September 22, 2003 there were 150 boats with more than $10,000 US damage. Before the storm was over, gales still blowing, an insurance adjuster was motoring around the anchorage and marinas filming all the boats with headsails, mainsails, or dodgers still on the boat. Everyone of those claims was denied due to the canvas being up during a named storm. Almost none of the boats had sails unfurl or dodgers blow off.
BUT - 2003 was the first year in which my policy (and I think most others in Western Mexico) contained an Addendum clearly stating that the presence of ANY canvas of any kind on deck during a named storm voided the insurance coverage. I knew the rule as did many others but a lot of folks never looked at their renewal info nor did they read the one page addendum that came with the renewal.
As far as I know the same addendum is still in effect - at least here in the west.
In 2003 - 2004 I pulled my canvas a total of six times. PITA... and the ONE time I didn't - well you know that story!