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
The mainstream of the aging research community theorizes on the basis of mountainous evidence that aging is accumulated damage. What that damage consists of is pretty much settled, but there is a lot of argumentation over how it all hooks together, what is important, what is primary versus secondary, and how in detail it connects to visible pathologies of aging.
Outside that mainstream, the present day accepted heresy, in the sense that the minority population of heretics are engaged with rather than cast out of the cathedral, is that aging is an evolved genetic program. It is a selected adaptation and where there is damage that damage is a consequence of epigenetic changes, not the cause of them. There are factions within this heresy too, and a lot of argumentation. If you want to learn more, look for the hyperfunction theory of aging and related thoughts as representative of the field. [1]
The damage view of epigenetic and signaling changes in tissues that occur with aging is that these changes are reactions to damage. Altering them may lead to short term benefits and be worthy of use as treatments but that doesn't do anything about the underlying damage - which will grow and kill you. In the case of stem cell decline with aging, this process is thought to be a cancer suppression mechanism, and thus forcing all the dormant stem cells back to work is going to mean cancer everywhere. Equally it may turn out that evolution has produced an overcompensation and some of the benefits of doing this might be effectively free. The fastest way to find out is to conduct animal studies in something other than mice (which are little cancer factories and have telomere dynamics that are very dissimilar to that of humans).
In contrast the programmed aging view is that reversing signaling and epigenetic changes is exactly reversal of aging, and is thus a great thing to be doing and we should be making full steam ahead on this front. I think they are wrong, and that the balance of evidence clearly points in the other direction, but as I said this is a heresy with enough advocates that they are not just ignored.
(Bizarrely, most of that portion of the mainstream who work towards enhancing longevity and slowing aging actually spend their time on potential treatments that make much more sense as goals for programmed aging enthusiasts. Look at sirtuin or calorie restriction mimetic work - all about altering protein levels and signals. All too few researchers take the sensible approach of looking for means of damage repair. But that's a whole different topic. I blame regulation of medicine as a force steering research into marginal channels).
Anyway, on to the heterochronic parabiosis, which is what you call the linking of circulatory systems in two individuals, one old, one young. This has been used for some years as a way of studying what might be going on in old tissues, especially in connection with the decline in stem cell tissue maintenance activity that leads to organ dysfunction and death. The end goal is to figure out the differences and use that knowledge to produce the part of the complete map of the molecular biology of the progression of aging that covers tissue signaling - most researchers in the field have no declared interest in doing anything other than looking at what is going on.
Along the way, however, someone will produce prospective treatments based on identifying signals to stem cells involved in the choice between activity and quiescence. No-one is going to be shifting blood around as a basis for treatments between young and old when you can instead figure out what exactly it is in the blood that is causing changes - this is a change likely to occur in the stem cell transplant field also, in which much of the benefits seem to depend on the alteration of signals caused by the transplanted cells rather than any cell maintenance they are doing directly. Why sling cells around if you can just manufacture proteins that have the same beneficial effects?
One of the signals is apparently GDF11, which has been explored for a couple of years now. [2] It is interesting to see that it is more general than simply localized to heart tissue. Given the large number of quite different stem cell populations in the body it would be unexpected to find much in the way of commonality between the signaling systems that they use. Apparently there is some commonality after all. Though I wouldn't hold out for much more. In general I'm expecting the exploration of cell signaling to be every bit as complicated as the hunt-and-peck approach taken to finding ways to interfere with cancer: a lot of proteins, different in most tissues.
[1]: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3455862/
[2]: http://dx.doi.org/10.1016/j.cell.2013.04.015