Big "meh" on this one.
I thought the idea was very interesting–a sentient species that only lives for a week–but it didn't really go anywhere. The premises could be used to examine lots of profound questions about the purpose and meaning of our lives, the impact of our actions on future generations, etc, all that stuff. And it had the potential to be very emotionally moving. The idea has an inherent element of tragedy, and tragedy often brings beauty with it.
But for all the potential, the execution was pretty dry, I thought. The protagonist accepts her lot with a stoicism that makes it seem simply normal, like this living a week and dying is no big deal to her, just how life is. She never seems really happy or sad or pensive about anything, and so I never got any emotional connection with her. She came off as just a freak, without any personality behind the weirdness.
I know it's not cool to harp on plausibility, but I think this is actually important to the story: The protagonist is obviously not human. All the differences (metabolism, life cycle, bearing only female children) are too extreme. She is a different species. So why does she need human sperm? Obviously, the male isn't contributing anything to the offspring, otherwise each generation of "mayflies" would be more human, longer lived, etc. This makes her quest to mate nonsensical.
A better (and more plausible) approach, I think, would have been to have male and female "mayflies" who live alongside humans, either in secret or openly. The contrast between their perspectives on life could have been fascinating. But maybe I'm asking too much: That sounds like a novel.