The log above just shows the jfbconnect.js file being requested and loaded by the user. There isn't any information in there about what's causing that script to be loaded (it could have just been a user reloading the page or navigating to a different one).
Is there any better log or information your host can provide as to what exactly is happening? We've never heard of this issue before from any user, but will gladly do what we can to investigate.
In general, when authenticating, there are multiple inbound and outbound requests to the social network provider. On a 'normal' page load for just viewing your site, there should be about 4 files loaded by JFBConnect (1-2 Javascript and CSS file, each). That's it. There isn't any mass-communication going on in the background.
I hope that helps. Whatever information you, or your host, can provide would be of immense help.
Thanks,
Alex