Peter,
Unfortunately, the error log isn't telling us anything of use. None of the errors reference JFBConnect or anything we're doing, which makes it obviously difficult to come up with a solution.
I mentioned disabling any JFBCProfile plugins above as well. Do you have any of those installed?
As for testing with another template, I understand you may be developing on a live site, but unfortunately, without narrowing things down, it's very difficult to proceed. Even if just briefly, you could enable error reporting and switch templates, that would help greatly. Another test with Rockettheme templates is to disable any of their caching, compressing, or other optimizations they do. Some of those settings are in the template, others are in the Rokzipper plugin, I believe. Once compression and stuff is disabled, and error reporting is enabled, we will hopefully see an error of what's wrong.
Finally, I'm assuming that you're not seeing any errors in the Local or Remote Error Check tools of Autotune, correct?
Thanks,
Alex