This is all pure speculation, of course. But could be fun to come up with. The only clue we have is what she says in Chapter 23: I could not be that awful. So, what does she have to give up? What does she fear? I'm 99% certain that at least one of the arches dealt with the throne of Andor. She had to walk away from her people while something awful was happening to them. I'd guess that another has to do with Gawyn. They're very close, and she obviously loves him, and I think it would crush her to walk away from him if he was in trouble.