I have this problem all the time. Clicking "Like" does absolutely nothing.
The solution is to refresh the page. Sometimes more than once.
I thought that maybe it had something to do with auto page scrolling and getting lost on "long" scrolls. But I've also noticed it on small threads where I'm trying to "Like" only the 3 or 4th post or so.
The only consistent thing I've noticed about it is that it's inconsistent.

Windows 7, desktop, Chrome