Hmm.. we'll have to look into this further as we haven't heard of this problem from other users. With that said, the invitation feature isn't as widely used anymore, so it's possible something broke and we just haven't caught it yet.
Can you confirm if the invitation is actually sent to the user and that the receiver can actually see the invitation in Facebook? Where are you seeing the invitation count as 0? In the front-end popup or in the administrator JFBConnect -> Requests area?
Thanks,
Alex