There's no way for JFBConnect to leave the user always logged in. Joomla manages the user's session and automatically logs them out after they have been inactive for too long. In the Global Configuration of Joomla you can set the Session Timeout to whatever duration would work best for you. While it's possible to set to 12 (or even 24) hours, I wouldn't recommend that high. That will cause lots of extra rows in your database and may slow things down eventually. Also, some users may want to be logged out automatically (friends house, shared computer, etc).
We use 120 minutes on this site, and know many sites that have the session timeout for 4-6 hours. The default is 15 minutes, which can definitely be too quick.
Hopefully the above helps, but if not let us know.
Melissa