Unfortunately, no, I don't have any other suggestions. Our SCLogin module uses the underlying Joomla authentication system if you're entering your username and password on that screen. So, if you're having issues with standard Joomla credentials, that means it's an issue with Joomla or another plugin (not the SCLogin module or JFBConnect). If the issue only happened with social authentication, that would be a different story, but I don't think that's the case.
The only other recommendation I can give is to check your .htaccess file. There are some directives in that file that can enable browser caching. If you didn't create that file yourself and had some automated tool do it, that could be the cause. You may want to try and get the original htaccess.txt file that ships with Joomla and try that, temporarily, to see if the issue goes away.
I hope that helps,
Alex