What is the significance of the first "mi'Neged"?
Rashi: She sat, not opposite him, but at a distance, as the Pasuk continues.
Targum Yonasan: It hints at the fact that, when she saw that Yishmael was getting worse, she threw the image that she had begun worshipping far away, and began Davenning to Hashem. 1
As Rashi hints in the following Pasuk. In other words, she returned to Hashem, and it explains why now Hashem answered their prayers.
How could she think that he will die? Hashem promised that he will be a great nation!
Hadar Zekenim: She had little faith. We find that she returned to the idolatry of her father's house.
רש"י: כשתי טיחות: מנין שהיה זה כשתי טיחות?
גור אריה: היו"ד של "מטחוי" היא יו"ד הריבוי.