I`m having the same problem with my blog http://vinterverket.wordpress.com/ . It also worked fine, but the last days its just a white blank box where the “Facebook Like Box” should be.
I have not changed layout or something like that. It just dissapeard.
I have the same problem with my page. It got so annoying that I decided to remove the like box. I tried everything possible ever suggested on the forum. The funny thing is I tried creating another blog (another theme) and there the like box worked fine but on the one I want it it’s still blank. Is there perhaps a time element for the themes? Like it stops working after a certain time?