Mike,
I have experienced the dropping of both visors while driving at different times. In addition to the SINGLE screw at the top on the ends, that you mentioned, watch out for the one in the middle of the scissor frame on the back. It goes through a bushing and in to the frame and comes loose often due to rough roads. Both sides have dropped while driving, without warning. The bad part is that the frame collapses, the bushing and the screw go flying and then Murphy's Law takes over. One time I had to look for hours with a really bright LED light until I found the parts.The last time I repaired that one, it got either Loctite or a lock washer. No problems since.