To speculate on the thread topic, my theory is that she became one of those theatre performers who always got good parts in the provinces, but never quite became a star. People noticed her performances, but never quite enough (perhaps she was too nice). Incidentally, could I just point out, that after the Roger Moore episode of TMS, Annie sue appeared in the film The Great Muppet Caper. And then many years later, in 1990 she was one of The Muppets present at The Master's funeral (she's in the CNN news footage of that).
Back to the truth, though, one might note that Louise Gold has puppeteered on various occassions for the Muppets on and off. But these days she's more often known as an actress in West End musicals. However, have you ever noticed how often bits of Annie Sue's delightful character her voice, have found their way into some of Ms Gold's other work. Sister Mary Amnesia on the OLC of Nunsense sounds awfully like Annie Sue. While more recently, in her cabaret act, she also used that voice in her Muppet medley.
Oh and one more note on this subject, see the following URL (about the musical Follies - I think it has some relevance since that show was about what happened to the follies chorus girls...),
http://www.qsulis.demon.co.uk/Website_Louise_Gold/Follies_Review.htm