John,
What SEF extension are you using? If it's not Joomla's core SEF, can you change the configuration of it to have it 'skip' JFBConnect. Pretty URLs really aren't required for JFBConnect, and can, on some sites, cause problems like this.
If you don't know how to disable SEF URLs for JFBConnect in your extension, let us know what you're using, and we'll try to give you instructions if we're familiar with how to do so.
Thanks,
Alex