I had the same or similar issues with the Like button. When I made a totally new post, Like’s worked. This was not the case with custom or migrated posts and pages, no matter what category they were listed under.
However, when I went and simply updated each of the posts. Note, nothing had changed, but I updated anyway…the Like button came back. I did not get the past likes back…as in those that were received while it was a WordPress.com post, but the Like option appeared and is fully functional on all of the updated pages and posts.
Edelleye.com