Can you check the following:
* You have the Social Profiles - JomSocial plugin enabled
* In the JFBConnect -> Profiles area, you have:
** Always Import Profile Data - Yes
** Import Avatar - Yes
** Import Cover Photo - Yes
If that's your current configuration, can you tell me if the cover photo was imported? Also, test mapping some profile data from Facebook into JomSocial. Once configured, let me know if any of the profile data is properly imported as well.
Knowing the above will help narrow down if it's a general connectivity issue or an issue specifically with saving the avatar from Facebook.
Thanks,
Alex