This is sort of a limitation of Facebook or at least the approach they want you to take. There is an option to request an offline_access permission, but that can come across very scary and really it's not what we're trying to do.
FB only gives us tokens that last for a limited amount of time. Eventually they'll time out, and FB will tell us that you're no longer logged in. We'll redirect you to the login page and you'll silently end up where you were. Unfortunately, FB doesn't seem to refresh that token while you're actually using the system. (At least it didn't seem to when I was writing the code; we're not using their full SDKs.)