It should be noted, when viewing one of the added admin tabs and the added admin tabs after it disappears, the corresponding main tabs in the group also disappear. This also includes the “Member Groups” tab of the BuddyPress Group Hierarchy plugin which also uses the BP_Group_Extension class.
This problem also seems to affect the Buddypress Group Extras plugin. After clicking on one of the above mentioned tabs under the group admin screen, the “Extras” tab also disappears, but when clicking on the Extras tab, all the (added) tabs before it shows up.
I recreated this problem on my setup. I am also developing a group extension and even it interferes with your admin screens. I can’t find any indication of what is causing this.
I’ll keep trying, but maybe someone else should have a look at this as well…