Yup, that's a common problem, unfortunately. Facebook's implementation of the Invitation widget is... lacking. We've tried to compensate for this in many ways. First, please ensure that the "Enable Automatic Resizing" parameter is enabled in the Invite module. If that doesn't immediately work, you may need to try altering the amount of columns or rows that are displayed.. I can't give specific guidance, as it can change slightly what may work on one site vs another (for various reasons).
Please try those options and see if they work. Looking at your page, I see none of the 'gotchas' that can sometimes completely prevent the Facebook Invite module from working, so we should definitely be able to fix you up.
Finally, thanks for the kind words about JFBConnect. We've worked hard to get it where it is, and constantly are improving it
Invite Plugin show up cutted
