Here's the key, when a female baby takes her first breath (oxygen in the lungs), a mechanism is set off that causes the ovi to cut off all connections to the mother body. To put it simple: before a baby girl takes her first sip of mother's milk, all the baby's children have become independent lifeforms, no longer connected to the mother's body. The baby's DNA will sabotage and boobytrap it's own ability to create new ovi at that point. This of course means, among other things, that their numbers are 100% fixed at this point. This means that at that point the number of fertility cycles her body will go through is a constant from that point forward. There is a similar, but more complex, process set off in men (in men, too, the cells that form the reproductive cells are very isolated from the rest of the body).
When a human is disconnected from the umbilical, a number of changes happen as a result of that in order to switch to what you might call internal power if it were a robot. The immune system wakes up. The lungs inflate. The heart starts actually pumping blood around (yes it beats in babies, but a baby would survive without a beating heart as diffusion will actually happen fast enough. This is really sad when it happens since the baby is alive at that point, but growing will kill it). Cell reproduction rates are massively cut, and are moving towards replacement-only (a 2 year old is -almost- no longer making extra tissue. An adult is simply a 2 year old with "stretched" cells, not more cells)
Essentially nature is trying to protect the next generation from DNA alterations by external influences. Menopause is just a side-effect that evolution doesn't care about because women are unlikely to have viable children at that age.
Further, all the eggs a woman will ever have are created while she is developing in her own mother. This is totally distinct from stem cells, many of which are able to generate new stem cells throughout our lives, albeit at an ever-decreasing rate.
[1] http://www.mayoclinic.org/diseases-conditions/menopause/basi...
While the principal author of that article published an equally-controversial paper in 2005, follow-up studies suggest that there are no newly-generated egg cells in mammals [1]. I think it's fair to say, again, that stem cells don't play a role in maturation of adult egg cells.
Changes in brain chemistry are another thing that's probably not directly damage related as the declines start around mid 20's.
PS: Biology has a lot of odd edge cases, youngest mother is 5 oldest 74. http://en.wikipedia.org/wiki/List_of_youngest_birth_mothers