All I know is one theory, where a crystal fetus or whatever it's called attached to her. Maybe I got that wrong so I could need corrections.
Another one I know is reincarnation which is not possible, but it goes like:
Aiz is a reincarnation of Aria and
Bell is a reincarnation of Albert.
Any others? or has this whole thing been solved? On how spirits can't have children so then why is Aiz alive.