The thing she s losing is her youth I think. Because the ticking of the clock implies that time is ticking away, just like her youth is.
Anne Sexton also wrote a poems about fairy-tale characters in which she implies that the ticking of the clock is fairy tales indicates that the characters are afraid to grow old and ugly. Anne has for example great sympathy for the bad witch in snow white who wants to be beautiful forever but sees that snow white is catching up with her. She also implies in that poem that one day Snow white also will lose her beauty and youth.