Moving this to the Graveyard because the issue has already been resolved. - However, if a situation like this occurs again please make a thread in the Bugs & Issues forum.
That being said, if the solution revolves around taking off 2fa, then I would recommend evaluating if the access of chats is more important than the overall security of your account. The mail function still worked which could've been an adequate solution of messaging people on Torn until the issue was resolved. If you did remove 2fa, I would also advise to make sure you've reenabled it, as the chats are working for all now.