I've often heard of a loose brace causing buzzing. But never I've heard of a loose brace causing damage because of the lost support.
How much of the bracing would have to be lost to make the lute (especially the soundboard) liable to damage? And, is there a "domino effect", where one loose brace causes the other braces more liable to come loose? To get on or off this list see list information at http://www.cs.dartmouth.edu/~wbc/lute-admin/index.html