It appears that our site is experiencing this issue as well. We have recently set up a couple of Private Thread Tags, listed players as we would when creating a private post, they get the invitation to join, but are often unable to reply to messages.
A few observations:
Someone who gets the message "Sorry, you do not have permission to post to this thread" MIGHT be able to to a quick reply using the new beta forum quick reply option.
People who were able to reply yesterday are suddenly unable to reply using the same method today.
I am unable to reply, even as the "owner" of the private thread tag.
The number of members of the private tag doesn't seem to matter. I have one with only about 6 people, and another with about 30. Both are experiencing the same issue.
-- Guild Leader - Taint & the Taint family of guilds.