Maybe not, but it appears that Ma has. (Mother Nature, that is.)
It sure seems to me, with all this Evolvin' goin' on, that She would have evoled Eternal Life, instead of all this death and sex and reproducin' and failin' and eggs and live births and.......
SO much simpler theory:
You ALIVE?
Keep at it!
Yeah, well, it sure seems to you wrong. The apparent reason that it seems to you wrong is because you seemingly cannot break out of your theistic mindset. If a Goddess existed, and was directing the course of life on earth, then it sure would make a lot of sense to make it eternal. But, in the absence of such a conductor, evolution merely requires that life procreate, and doesn't have any reason to evolve 'eternal' life.
Moreover, it would require a substantial degree of alteration in the fundamental architecture of terrestrial life, and there is no environmental pressure that would cause species to evolve in that direction. It could not happen by accident in a multicellular organism. You would basically require an organism that either perpetually grows or perpetually rejuvenates itself, and either case would demand an impressive degree of modification, and create significant problems in terms of viability (resource limitations would be one, and a static organism cannot adapt to a new environment).
These are problems that we can likely handle due to our higher intelligence; a trait which is absent in other organisms. Finally, if we attain eternal youth via technology, it will be because we evolved the capability to do so (something that's almost certainly already happened). Therefore, evolution will have produced what you say it hasn't. If you're confused, go back and reread my point #2 above.
PS. And with many unicellular critters that reproduce by splitting in two (binary fission), one might say that they are already 'immortal'.. There are also essentially 'immortal' cells - stem cells and cancer cells by example - which will abide so long as they receive sustenance.