Delaying menopause might be bad for longevity because you'd be exposed to more estrogen. Excess estrogen increases your likelihood of developing breast or ovarian cancer.
You forget though that offsprings of humans are a result of a disability to survive limitlessly, and offsprings are the closest thing to survival of yourself. Once we have no limits, not only there is not a good reson to have children, it is also problematic considering over-population. It is more reasonable to avoid the life if a potential creature, that is not even aware of that and has nothing to lose yet, than to limit an already living being, that has everything to lose.
I know it is not related, but it might solve the problem indirectly.
-Inf.
I don't know if people would stop wanting to have children if they had unlimited lifespans. Personally, (if there were enough resources to support new people) I would be
more likely to reproduce if neither I nor my child would have a restricted lifespan. It might be nice to share an eternal life with a child or two but I can't imagine spending a huge chunk of an already finite life raising a child who will ultimately die. Of course, I'm obviously not representative of the general popolation.