>>13228655 I never got why Mai was allowed to keep her Child right after Tater died, but Shiho was eliminated as a Hime.
Childs are powered by the Hime's feelings for their most important people.
Mai is basically the nicest and most caring person in the entire show. EVERYONE is important to her, so even after two of her most important people got green-sparkled she could still summon Kagatsuchi.
Same reason why Kagatsuchi went into super-mode and resurrected her like a phoenix when they got hit by the satellite cannon.
She loves so much it gives her a hell of a lot of power.