Hmmm.. I thought I was logged in due to the redirect to the blog. I just tested again, and it seems like I wasn't.
Here's what I'd recommend to narrow things down further:
1) Set the "Enable Debugging" setting in JFBConnect to "Yes". That may show an error message when the Login flow occurs. If so, let us know what that message is as it will help narrow things down.
2) Disable any caching you may have enabled on your site. Specifically, if you have the System - Cache plugin, disabled that. However, disabling the Global Configuration caching or any other extensions would be good to test further.
3) I'm being redirected to the Blog after login. Is that how you have the JFBConnect "Returning User Redirection" setting in JFBConnect configured? If not, we'll need to determine what is causing that redirect as it may be interfering with our full login flow.
I hope one of those helps solve, or at least shed some more light on, the issue.
Thanks,
Alex