It looks like the div for the JFBCSocialShare belongs to your main container, so it is only clickable when you scroll down to this element.
Could you try adding the following script to the module default.php file? It will attempt to put the module right before the closing body tag so it's outside of every other div. We do this in SCLogin, but haven't had anyone report this as a problem for this module.
<script>
jfbcJQuery(document).ready(function() {
jfbcJQuery(".jfbcsocialshare").appendTo("body");
});
</script>
Let me know how this goes.
-Melissa