We have banned her many times. Banning her encourages more socks.Have you considered banning her and not letting her post on your site and annoying everybody?
Most places just ban the ban evader when they pop up again, not let them run around and continue to cause chaos.
You could also say that if people give attention to her, you will ban them also to discourage her to come back.
There are definitely things you can do about it, you just don't want to for some reason.