We're not sure how JFBConnect would be related to this problem and we haven't heard any other reports of such an issue. On your page, as Melissa noted, the Twitter buttons are not from JFBConnect at all.
If you think there's a conflict with JFBConnect, the best way to eliminate JFBConnect as a possible source is to disable our JFBCSystem and JFBCContent plugins. Those plugins are what enables all of our features, so disabling just those plugins should let you test as if JFBConnect isn't enabled at all. If the count re-appears when those plugins are disabled, let us know and we'll gladly help investigate further.
Thanks,
Alex