Essentially we didn't live long enough for the menopause to be a problem. The average age of death for women through much of history has been 30 to 40 years. It is really in the last few centuries with improved health and hygiene, diet and the ability to survive childbirth, that people have more regularly lived to the menopausal age group. All that the evolutionary forces require of someone is that they live long enough to breed, bring up their children, and be around to be a teacher and a protector for one's grandchildren. For most centuries this whole process was over and done with by the age of the menopause.
The basic reason women become menopausal is because they run out of eggs. Women are born with a contingent of egg follicles, and from a few months after birth onwards there is a gradual decline in these egg numbers.
This is not all because the eggs prepare for ovulation and shed, although this certainly accounts for a lot of the eggs. In simplistic terms women start releasing eggs at the onset of puberty and every month will prepare numerous eggs, one or two of which will actually be released for fertilisation. Many more than this though will slowly die off from the ovary. In general terms we release good eggs first, and the more abnormal, harder to stimulate eggs are released later.
By the time women approach the menopause many of the egg follicles are resistant to stimulation, and this essentially leads to fluctuations in hormone levels and irregularity of timing. When the ovary finally runs out of egg follicles it is no longer able to produce hormones on stimulation by the pituitary gland (the organ that controls the whole process) and oestrogen levels drop and periods stop. Resistant follicles will sometimes continue to make oestrogen at odd times after the apparent cessation of periods leading to the occasional delayed period like post menopausal bleeding.