Death is the great non-moral evil. Therefore, the problem of non-moral evil is, in the main, the problem of death: Is an omnipotent, omniscient and perfectly good being likely to allow death?
But not all death seems to be a problem. The argument: "Grass dies, therefore God doesn't exist" seems unconvincing (why? because the death of grass isn't a bad thing? because it's necessary for evolutionary processes that organisms die?). We are only really bothered by the problem once we deal with critters that are conscious and capable of sophisticated lives. It is not at all clear that the world would be better if mussels lived eternally and did not reproduce—it seems that an ever-refreshed generation of mussels is no worse, and may even be better aesthetically.
So, now, let's think about an evolutionary sequence, and see if we can come up with a problem for God. Algae and other simple critters evolve, with individuals dying, and their deaths essential to the evolutionary process. And we are not bothered theologically by their deaths. We get more and more sophisticated critters, until eventually we get to ones where we're bothered theologically by their deaths (maybe only humans fall in this category, or maybe it is a rather larger class). Consider the case of the first of the more sophisticated critters, call him Jake, whose death bothers us theologically. (Maybe Jake is Adam, or maybe Jake is some whale, or horse, or whatever.) If we're bothered theologically here, it's apparently because we have an inclination to think God should have acted differently here.
But how should God have acted differently here? I see two suggestions, the second coming in two sub-options.
1. Maybe God shouldn't have allowed the mutations and recombinations that led to Jake's existence. Maybe he should have kept the critters of the world below the level of sophistication at which death worries us. But that doesn't seem what God should have done—indeed, the world without Jake does not seem to be better than the world with Jake, and in fact the world with Jake seems the better world.
2. Maybe God should have given eternal life to Jake. But how? One option is that he can give Jake an eternal life after the end of his normal lifespan on earth. But if the atheological argument from death is predicated on the concern that God didn't do that, then the argument needs to be supplemented with evidence that God didn't do that. And such evidence is not, in fact, available. (Imagine that someone argues against theism: "God, if he were perfectly good, would create physically undetectable persons." Surely the right retort is: "If so, what evidence do you have that he didn't?") The other option is that God can either miraculously sustain Jake forever on earth or modify his nature and environment in a way that allows him to live forever on earth. But this, obviously, leads to a problem of overcrowding, which would, in the end, require some of Jake's descendants to be transfered to somewhere else—unless God also took away Jake's ability to reproduce, or took that ability away in the descendants. But the suggestion that what God ought to have done is to modify Jake or his descendants so he can live forever on earth and cannot reproduce does not appear morally compelling.
If these are the main alternative suggestions, then there is no atheological argument to be made from Jake's death.
Objection: The problem isn't death, but early death.
Response: I think this is mistaken. First, suppose I lived a million years. And finally it's time for me to die tomorrow. Is that death any less fearsome because it was preceded by a million years of life than if it were preceded only by 70 years? It does not appear that a merely finite extension would help. (And of course we have arbitrariness problems here: How much should God extend the life by? However much he extended it by, we could complain that there should be more.) In fact, if anything, a death after a million years would be the worse. (Consider how we feel about cutting down a 300-year-old tree versus cutting down a 10-year-old tree.)
Against my response, however, there is an intuition that there is a time for people to die—a time at which continued life has a diminished value. So the evil is not so much an early death, as a premature death—a death prior to reaching that time. So, the suggestion goes, God should not allow Jake or anybody like Jake to die a death prior to reaching the time at which continued life has a diminished value.
I think this suggestion incorrectly—and offensively—downplays the life of old people. But let me push a different point.
Suppose Jake was struck down in the full possession of his faculties, and consider instead the allegedly better life where Jake at age a starts to live with a life of diminished value, and then at age b finally dies. Now consider Jake just before age a. He is, on this story, facing a future of diminished value, followed by death. Whatever he gains from the fact that he suffers death at a time at which his life is of diminished value rather than in his prime, he loses by the fact that he is facing a diminishment of the value of his life. Both the Jake who is struck down prior to the diminishment of his faculties and the Jake who is struck down in his prime are facing a decrease in the vigor of their life, from full vigor to zero. Granted, one is facing a more gradual decrease, but the same complete destruction of life's vigor faces both.
Perhaps, though, the distinction between a premature and a non-primature death is to be accounted for differently than by reference to the diminished faculties in old age. Maybe the problem with a premature death is that one hasn't yet accomplished life's tasks.
So now the problem of death is this: Why does God allow Jake to die prior tot he accomplishment of life's tasks? Note that if that is the formulation, the problem is only really pressing if Jake is human. We do not attach a great value to a non-human animal's accomplishment of "life's tasks". We do not, for instance, feel that a great harm has been done to an animal if we render it infertile (in a humane way).
So what are life's tasks? There are three possible families of answers: (1) the tasks that are one's individual vocation, (2) tasks like education and reproduction prescribed by human nature, and (3) one's own personal goals. Option (1) will, if anything, harm the atheological case, because the notion of a vocation is, I think, essentially a theistic one, and so the existence of such tasks, if admitted, is an argument for the existence of God. Moreover, if one's tasks are the ones set by God, then who are we to say that Jake died prior to finishing them.
Option (2) is more promising. It presupposes a broadly natural law perspective that not all will share, however. But let's be concrete. What are these tasks? Obviously, the main one is the attainment of virtue. So then the claim is that what is a problem is a death prior to the attainment of virtue. But this makes much, though not all, of the problem of death a species of the problem of moral evil—the problem of why it was that one didn't develop virtue before death (the case of children is different, though). Moreover, questions of the afterlife become relevant, since the task of virtue can, surely, be continued. Besides virtue, what else is there in life's tasks? I think the main ones are: wisdom and reproduction. So is the problem that of dying prior to attaining wisdom and prior to reproducing? The wisdom case is, however, often (though not always) a matter of moral evil—one hasn't gained wisdom because one hasn't been pursuing virtue and wisdom sufficiently. And, again, the afterlife is relevant. Finally, there is reproduction. But I do not think we worry as much about the evil of dying childless as past generations did. In any case, it seems that in a case of dying childless it is on the dying that we are likely to focus.
Or maybe human nature sets us not just tasks, but also goods, and we should sample them. But I think the main goods that ought to be found in a full human life are, in fact, virtue, wisdom and progeny (though some may forego the literal attainment of the last, for the sake of the Kingdom).
The last option is of fulfillment of one's own goals. The suggestion is that we set some finite set of goals for our lives, and a full human life is one where we fulfill them all, and what is problematic is a death prior to the attainment of all, or maybe most or some, of these goals. I do feel the force of the idea that there is an evil in a death "with much undone." But I do not think personally set goals have great moral weight, unless they happen to match up with a vocation or with basic human goals—which would bring us back to options (1) or (2). Why should it matter much, to me or to anyone else, that I have set something as a goal for myself? Moreover, is it not very much bad to be cut down before one could set a goal to oneself. But surely whatever finite goals one set for oneself, after fulfilling them, given a longer lifespan, one would set more goals—or else sink into depression.
All in all, I do think the non-moral evil par excellence is death. Not early death, not premature death, but death. A million years of life followed by death exemplifies this evil just as a day of life followed by death exemplifies it. However, if we think about the evolution of Jake, it seems that the option of allowing Jake to come into existence with a finite lifespan, and then continuing Jake's existence elsewhere, is either the best option, or no worse than any other.