Technically, there's no reason that organisms
should reach a point where they're "no longer able to reproduce"; I think it's merely a random choice of our most basic biology that we grow "old" and then die from various diseases and systems failures, rather than simply surviving until there are so many [generations] of us around at once that some individuals can no longer find food. This is the way that asexual species, like bacteria, function.
You'd think it would actually be in the best interest of any given organism to have as long a reproductive lifetime as possible, and therefore fitness would increase along with longevity, as long as that longevity remained virile/fertile.
Then again...
If the old did instead survive to compete with the young, evolution would start to fail as a process—you'd have too many non-adapted organisms reproducing with one another, and so what adaptation there was would happen much more slowly.
Today, sexual species that have "dropped back down" into being asexual, reproducing by cloning or the like (which have the same evolutionary disadvantage as a non-aging species would have, but more so) can survive and prosper. However, far enough back in the genetic soup, when sexual species first diverged from asexual ones, there was probably a fierce competition where being a sexual species was only a little better (it requires more resources, after all), and so aging provided an immediate advantage in terms of setting an equilibrium point for species size, so as to not strain resources.
(This may very well be taught in an intro Bio class, but I love discovering things on my own in the form of meditative writing. It's a fact completely untaught in schools today that knowledge lies at your fingertips that you're completely unaware of, not from a book or a website or another person, but from your own mind, and that you can access it without having to have anyone guide you to it. Philosophy is neglected as a means to pursue ordinary, practical knowledge, but it's really just a super-set of science: there's still a hypothesis, experimentation, observations and a conclusion, it's just that the "experimentation" doesn't require a physical world. In the case above, obviously, it would be better to have an actual scientific study, but the very fact that you can derive a preliminary intuition of a topic without anyone telling you what to think, or giving you a demonstration one way or the other, is revelation enough for most people in the world today.)