Couldn't it be just a relatively large object, anywhere in the interstellar space between the star and Earth? I mean, look out the window at a far away car or a tree, then stretch out your hand and you can block it entirely with your thumb. What if the 'thumb' is that object (a planet, a star, a comet, some space debri, etc.) that's between Earth and the star, and it's just the right size to only block that star, and no other stars. Why has this very simple explanation been ruled out (if it has been)?
I know that the debri next to the star explanation has been ruled out because of the lack of IR that would come from that debri being heated up if it was close to the star. But this is not a problem here, if the blocking object is far away from the star.