I left the Alakol Homeowners Association since I no longer live there. It still appears on my group list and profile page. It is invite only. If I open it, I have no "leave" option, so I am out. It is just still listed among groups to which I belong.
I thought maybe it was just an issue with invite only groups, so I left six or more regular groups. They all dropped from my list, but Glitch Addicts still remains. Initially, I entered it by invite. I tried rejoining through the page and leaving again, but it is still there.
Nothing against any groups; just testing.