Several of my sites got hit by the "thin affiliate" penalty. Can they recover?

This might not be the thin affiliate penalty.. and possibly just a google dance. If this is the case get some unique content on soon as possible to avoid the penalty.

Also something else to consider.. I had a problematic host which was causing my sites to be slow. Google doesn't like this and I saw a similar pattern of unranked, ranked again, dropped rankings etc. until I sorted it out. So check the speed of your sites (you can do this via google webmaster tools).