Miyax's most life threatening predicament is survival. She decided to run away from home and head toward San Francisco to meet her pen pal. Unfortunately Miyax became hopelessly lost. She is way out in the middle of the tundra with winter approaching. She has minimal food supplies and does not have the proper food and shelter stuff to endure the coming winter weather.
Miyax's other predicament is a cultural one. I wouldn't call it desperate, because it's not life threatening in terms of stopping her heart from beating. But it is life threatening in the sense that Miyax feels that she can't "live" her life the way that she wants to. It's a bit of a twist for the reader to watch Miyax run away from a traditional Eskimo marriage. She doesn't believe in such things. A reader would think that she is making the push toward being more modern. But after spending the winter on the tundra with the wolves and having to use the traditional Eskimo ways to survive, she has a disdain for modernization. She is appalled that her father now hunts with modern tools, so she runs away again to be more traditional.