Sorry for the delayed response.
As noted, JFBConnect does have ways to keep the user logged in as does Joomla itself. However, all of those methods work on setting cookies on the user's computer. If you are closing your browser and restarting it before you try to login again, in some cases, that can clear your cookies for a site preventing the automatic login functionality.
There are many privacy considerations that browsers take into account when determining how cookies should be used. Additional privacy options for when to clear cookies and browsing history by the user can make it more difficult to keep a user logged in. That's the purpose of those privacy settings though, so there'd be little we could do to 'fix' that problem if that's the cause.
If you can describe your use case, that would help us understand the issue more:
* What browser are you testing with?
* After you login, how do you test re-logging in? Do you use the 'logout' button on the site, do you close the tab, do you quit the browser, do you restart the computer, etc?
Thanks,
Alex