The fitness that evolution is driven by and toward is "reproductive fitness".
That is, species are driven by natural selection towards those traits that increase the likelihood that they survive long enough to produce offspring that themselves have a reproductive fitness greater than or equal to their parents.
So natural selection just does not care anywhere close to as much about what happens to an organism after it successfully reproduces, except to the extent that sticking around to raise its offspring improves the reproductive fitness of its offspring and thus its own fitness.
For pretty much every species, there was never any selective pressure to improve physiological maintenance mechanisms beyond what was necessary to achieve the above. So our short-term maintenance mechanisms are fairly robust (e.g., healing injuries, especially while youngish), but longer-term we still have issues with cancer and cognitive decline because the sorts of maintenance needed to prevent them were never selected against except while we were old enough to be parents.
So evolving to "not age" happens, but only to the extent that it improves the reproductive fitness of the population, and usually not much further than that.
As far as the whole migration issue, it's likely just more likely for animals to evolve to reproduce more often than to live longer if there exists a sufficiently large ecological niche for them to occupy. Changing the frequency and degree of reproduction is much easier than fixing aging.
The above was a fairly superficial examination of the issues and there, of course, exists more nuance if you look for it. But I hope this explains the basics.