An interesting idea here, but two things distracted me from liking it more:
1. The complete lack of ending.
2. I'm getting sick of stories that jump forward and backward in time like that. It's done way too often already, AFAIC. I rarely find it as compelling as a chronological story because in the past sections there is very little tension--we know where we end up so all that's left to do is infodumping, usually. It works even worse in audio because it's often unclear where the section breaks are, leaving me confused at regular intervals when characters that I thought to be dead suddenly reappear, settings change with no explanation, etc...
3. The nagging question of trying to understand how all the genetics work took up most of my thinking time. I kept wondering how such a gene would even develop in a species. It doesn't provide any evolutionary advantage, in fact gives a disadvantage in making finding mating pairs much more rare. So how would it develop in the first place?
--I tend to think that raetsel is right, that it would affect the population on a much slower scale than the story suggests. Take into account that for the population to get down to 3% the previous generation's men would all have to have died already. There would be a lot more cases of one man having multiple sex partners, and them being a younger age until that point, but there should be plenty of time to diagnose the problem before it becomes intractable.
