I'm sorry for the delayed response. We've tried to recreate the issue, but haven't been able to. Unfortunately, we don't have any truly active groups to test with either, which may be part of the problem.
From everything I can tell, this seems to be an issue with Facebook, as noted above, and their privacy settings. I don't believe this has anything to do with upgrading JFBConnect as there were no changes in the 6.1.1 or 6.1.2 releases regarding the Groups feature. We'll gladly even send you the older 6.1.0 release if you'd like to re-install it and test if downgrading it fixes the problem.
It's strange that some posts work, and some don't. Again, all I can think is that there's a relationship between the user you set the Channel up with and the users that are posting in the group, but I'm at a bit of a loss.
Here are some posts on Facebook's own community describing the same issue. I'd recommend reading through a few to see if the solutions there seem like they may help you as well:
www.facebook.com/help/community/question/?id=497635546949052
www.facebook.com/help/community/question/?id=639234999435995
www.facebook.com/help/community/question/?id=212058152281325
www.facebook.com/help/community/question/?id=4903464998710
I hope that helps, but definitely let me know if you find anything.
Thanks,
Alex