I remember reading some information about evidence to indicate that some stem cells survive in human females which lead to some eggs being produced through life. It's a rather newly discovered piece, though, and I saw little more than a mentioning of it.
Regarding menopause -- I've read about the "grandmother hypothesis" which stated that as humans' cultures became more complex, older individuals' stored information became a valuable asset among early social groups. Those females who ceased ovulating incurred the cost of ending their reproductive lives, but also the benefit of a decreased risk of mortality and an increase in how long they were able to continue teaching their children and grandchildren, increasing their survival rate.
Some think that menopause is simply a side-effect of having a reproductive system that worked well enough for the average lifespan of our ancestors but simply breaks down by about age 50. It's possible that the fertile years used to last throughout the average lifespan when that's how long our ancestors lived, but did not extend as far as lifespan increased. While the great apes do not experience menopause, they also reach "human menopausal age" very, very rarely. Perhaps menopause is more the result of maintaining a derived ovarian cycle that simply did not extend along with life expectancy. In any case, we must remember that not every trait or characteristic is necessarily beneficial -- sometimes it's more of a by-product of selection for something else, or simply has a neutral effect. This reminds me of the question "why does menstruation occur only in humans?"