Not sure why you're encountering that issue. It's not something we've heard of before. There may be a very simple fix for it though, if you're up for a quick code change.
Please edit the /components/com_jfbconnect/includes/jfbconnect.js Around line 874, you'll see:
jfbcJQuery.ajax({url: 'index.php', data: url}).done(callback);Update that to:
jfbcJQuery.ajax({url: jfbc.base + 'index.php', data: url}).done(callback);That should make sure the AJAX request always goes to the root of your site, not the current base URL.
Let me know how that goes, and good luck!
Alex