However, from time to time, its Facebook connection functionality doesn't work propertly. This is not a good thing for a community where some of your users are connecting using FB. As I told, the good performance of this functionality is random and it depends on what you are updating or installing on your Joomla (I think).
Once you see that something is going wrong you decide to ask for support and then you discover that nobody answers or they answer late and with vague responses (in this particular case). This is not acceptable if you are running a community and you have spent money on advertising. Not professional.
So, in summary, if you are looking for a community component to build an small and isolated comunity and nothing else, maybe Jomsocial will be your component. But if you are trying to expand its potential using FB users it's best to combine it with other solutions (and spend more money).
Do not try its support desk and forums because it's really bad.