The thing is that he is getting sick from exposure to "new" bugs. If you move him, he will have to start all over with the different bugs at the new care place. I know it is awful to have a sick child (not to mention inconvenient), but it is actually good for their immune systems to be exposed to things early. There have been studies showing lower rates of leukemia and things in children who were exposed to other kids under age 3 as opposed to school age. And the good news, is that he is building up immunity, so he should start to get sick less often once that immunity has built up. It won't be this way forever. And it sounds like you must be pretty close to coming through the other side of it.

If he enjoys where he is, I wouldn't rush to remove him. Stick it out for another month or two and see what happens. I have heard that kids who don't go to day care tend to be sick a lot during the first few months of kindy or school instead, so hopefully you won't have to worry about that in a few years!