There's a bug with the Invite module in 1.6 that we're hoping we've already fixed. We fixed it successfully in the 1.5 version and are planning to release a similar update for 1.6 soon. If you could, in the /modules/mod_jfbcinvite/tmpl/default.php file, at line 40, change the following:
Change the class to an id
When done, the line should look like:
<div style="position: relative; top:0px; left:0px; width:<?php echo $closedWidth;?>px; overflow:hidden; z-index:100" id="jfbcinvite">
Hopefully, that will fix you right up, but if not, let us know!