Sometimes, pushing the show desktop button will hide AWN itself. This clearly won't do. A way around it is to open up the compiz configuration menu (if you haven't got it installed, it's usually called ccsm or compiz config settings manager). From there, select the show desktop feature under the "Desktop" heading.
Go to the "Misc. Options" tab, and append the line "& !(class=avant-window-navigator)", without the quotes, to the window types list.
Exit compiz, and AWN's show desktop button should now work as expected.