Chris,
Thanks for the PM with your site address. Knowing that, I have a different change to try. Still unsure why it's doing what it's doing, but this should definitely fix the problem. Please edit the same /plugins/system/jfbcsystem.php file at around line 370. In there, change the line to:
$newText = '<link rel="stylesheet" href="/components/com_jfbconnect/assets/jfbconnect.css" type="text/css" />' . $newText;
That should remove the domain path altogether and simply load the file as a completely relative link. If that doesn't work, please try disabling SEF URLs completely and testing again. If that works, re-enable the SEF and let us know. That will simply help us narrow down what's causing the link to revert back to non-SSL.
Thanks,
Alex