I had the same thing happen to me, a site that has been #1 for years on a few key terms and in Dec I noticed it drop to #2.
The #1 site has a .org that is an exact duplicate of their .com on the front page and a few internal pages. There is no unique content whatsoever on the .org. If you click on a menu item of the .org, it takes you instead to the .com.
Inside the header of the .org's main page is an base href= pointing to the .com. The other duplicated pages do not have a base href (or 301, 302, etc)
The .com has one main link pointing to the .org
Both the .com and .org are pr3
It looks as if the .org has pushed the .com to the top even with duplicate content.
Loophole in using a base rather than a 301?
I'm still researching this and will write back when I find more, but I had to share my frustration when I read the title of this post!