This is a great question. The narrator clearly tells us that she owes her "existence" to her mother three times, yet in the story she only explictly refers to the first and second way in which her mother saved her, telling us of how Anna saved herself from a tragic circus accident that resulted in the death of her then-husband, and then secondly refering to the fire that threatened to burn the narrator when she was a girl. The narrator at no stage in her narrative explicitly tells us what the third time was, however, if we look at the story and the narrator's present state and why she has come back to live with her mother, perhaps we can infer that this third time is the way in which her mother's solitude has given the narrator the excuse that she needs to flee her life and return home:
Since my father's recent death, there is no one to read to her, which is why I returned in fact, from my failed life where the land is flat.
We are given no more details about the narrator's "failed life," but given the way in which the narrator is similarly unforthcoming about the third way in which her mother saved her life, perhaps we can connect the two. The death of the narrator's father and her mother's need for somebody to read to her could have enabled the narrator to escape from what appears to be a very difficult and painful situation.
The third way was that she saved her from the burning farm house using her trapeze skills. :)