I just used the SCLogin module on your page to create a user with my FB test user credentials. I then logged out and was able to log back in again just fine. You can see the user in the backend with "Melissa Lynne SourceCoast"
Please provide more detailed steps on how to reproduce the behavior, a specific URL to test, any error messages that you're seeing and expected vs actual behavior.
The warning that you're seeing about the Graph API should not be the cause. For Graph APIs, once a version is no longer usable, any calls made to it will be defaulted to the next oldest usable version. So for example if JFBConnect is calling v2.2 and it was no longer available as of March 25, v2.3 will be used. The changes in the 2.3 version shouldn't break login. And as I mentioned, I am able to log in with the test user without problems.
-Melissa