Please try switching the JFBConnect backend > Configuration > Facebook > "Show 'Login Credentials' in popup" to No. This will redirect to a Facebook page to perform the login and then back to your page. Usually this is enough to fix the issue on mobile devices, but please let me know if this doesn't help.
Also, please turn on Error Reporting in the Global Configuration area to see if there is a PHP error. Usually a blank page will indicate a fatal PHP error that's being thrown. If there is a message, please provide the full text of it.
-Melissa