Dani,
You're site is using multiple Facebook extensions on it, and they're confusing Facebook. If you open the HTML on your site, and search for "all.js" (the Facebook Javascript library), you'll see it's being loaded 3 different times. Additionally, in the area of each call is a reference to appId. You're using 2 different Facebook application IDs. Because of this, Facebook doesn't know where a user would be invited too (first application or 2nd), and simply is refusing to load the Invite module.
Please disable some of the other Facebook widgets your using. Hopefully, there's a replacement available in JFBConnect that suits your purposes, but if not, let us know!
Thanks