When Panda was being rolled out some pages on my site were hit hard but not the entire site and after various attempts to repair the damage it seems that it's what the user does when visiting the page that moves the pages in and out of the rankings.
The pages were primarily product pages with links to another site for purchase, a typical affiliate setup. The majority of the time when a visitor lands on one of these pages they wind up clicking through to the other site, assuming they don't bounce. It would seem that adding other options and making the downstream click NOT be to a single site can pull pages out of their pandalized state.
From a search engine perspective cutting out the middle-site to get visitors where they will ultimately end up more quickly makes sense. It would also make sense that the downstream site receives a boost for various keywords since it is where visitors looking for that keyword end up. Nofollow or not, perhaps just a mention and not even a link, may be enough to give the downstream site a boost and take yourself out for the given keyword.
For the above to hold true Google would need to observe a high percentage of visitors ending up on site B from your site in order to determine that they should be returning site B themselves. If your pages send a high % of your visitors to the same 3rd party site you may want to try and provide other options (mashup sites still do well well) in order to keep the % of visitors to any given site lower. It worked for me.
