On our cars there is a plastic "ice cooler" housing the top folds into. It is viewable with the trunk lid open. This is the same housing that can be retracted from the trunk up and into the tonneau area when the top is up to give more room in the trunk.
On each side of the housing is a metal frame that supports it. There are two round metal arms, one on each side, that slide over a short axle and are secured by a flange. (See the picture below) The flange tends to work loose and these arms can work their way off the axle and dangle/rattle. If the arms are simply put back in place, secured with the flange and the flange is secured with some light duty Loctite that may quiet your rattle.
Note that when the flange works loose, it will fall into your trunk down into the carpet. With a good flashlight, you should be able to find it.
In the pic below, you can see the passenger side arm clearly (aluminum color) with the problematic flange attached at the end of the axle. If the flange works loose, the arm vibrates off over time, comes off the axle and dangles loose in the trunk.
Well, the board will not let me add my Flickr URL so I can post the picture. Any suggestions, anyone, on how to post this photo?
Here is a link to the photo, so just click on it and the photo should show make this clear: