To establish a case for an adaptive post-reproductive life-stage, one needs to show (at least) the following things:
(1) Prevalence: Across environments, but especially in a wild or non-protected environment, the population experiences more post-reproductive lifespan than is expected due solely to demographic stochasticity.
(2) Utility: Post-reproductive individuals do something selectively advantageous, such as helping younger kin to survive or reproduce.
In many cases, one would like to also address
(3) Advantage: Those individuals who become post-reproductive have a selective advantage over same-age individuals who simply continuing reproducing indefinitely.
However, this third is more complicated, because in many cases there are no individuals who fail to stop reproducing to compare to. For example, 55 year old women giving birth are rare and not easily compared to those who stopped at a more usual time. So testing (3) requires extrapolation and counter-factuals. This assumes that if continuing to reproduce past the current age of cessation were selectively advantageous, that the species' reproductive physiology would allow for it. In many cases, theoretically advantageous traits simply don't exist in the population, and therefore cannot be selected for. If the choice is not between ceasing reproducing or continuing, but rather between ceasing and being useful or ceasing and not being useful, useful wins.
So we are left with basically two fairly simple tests to make decent case an adaptive post-reproductive life-stage. And after some decades of interest in the evolution of post-reproductive lifespan, for how many species has this case been convincingly made? By my count, three. Humans, orcas and a gall-forming social aphid, Quadrartus yoshinomiyai. There are several other likely candidates. Short-finned pilot whales, and possibly other social cetaceans. African and Asian elephants. But I've become very interested in a much more accessible and experimentally tractable species. It lives in multi-generational groups of (very) closely related individuals. Individuals play subtly different roles in the group throughout their lives. Older individuals stop reproducing and can (assuming no one comes along and kills them) live for extended periods post-reproductively (on the time scale these things live). You may have it in your garden.
Any guesses? Later this week I'll give you the answer.