A sharp decline in female fertility would eventually destroy monogamy, but only near the very end.
If as @Fattie asserted, the gestation potential fell to 3 opportunities per lifetime, and if the likelihood of pregnancy remained unchanged, then a sharp population decline would result.
Most women would have no children, while a few might have one and a extremely small few might have two.
Within a few generations, our current billions could become tens of thousands.
If during that decline, our doctors and scientists were unable repair the gestation potential, other solutions would need to be pursued.
Artificial insemination during all three opportunities would become mandatory with state aid provided for the raising of all resulting children.
99.9% of all artificial inseminations would be made female with y-potential sperm being filtered out of the artificial gene pairing process.
A small population of males would be raised in each generation to maintain the sperm supply, but those numbers would be kept small to focus most of our species resources on population repair.
Monogamy would not be a generally available possibility for dozens of generations. So when the population finally rose above the extinction threat, and the artificial inseminators could finally allow a higher percentage of males to be born, there would be little social demand for monogamous pairing.
Having men remain a one in a thousand cultural anomaly might just remain an ongoing norm. As a sever minority, we might even loose the vote, fair wages and eventually our right to work; reduced to being arm candy for the powerful women who can afford to keep us around like pets.
After all, nature loves a little irony.