How does Christianity explain suffering that ends in death? Does suffering in this life really matter?

How can suffering from natural causes be reconciled with an omnimax god?

Both answers above contain the major theme of God refining us, making us more like Him, so that after the period of suffering, the person is better than before. Now, both assume there is a period after suffering, where the person can use the lessons learned (and for many that is true).

However, there are many cases of people who suffer terribly in the world (for some, almost analogous as if they were in Hell on earth) and do not get a chance to use their "refinement". 

There suffering appears pointless, sad and for many people - goes on until there last day here on earth.

In the second question, @MasonWheeler answers that it is in "preparation for the eternal world" (assuming the person is a Christian, I guess....)

This answer makes it sounds almost as if this life here on earth is completely irrelevant. (To me that sounds very dangerous way to view life but would be for another question.)

In any event, how does Christianity explain suffering that ends in death?
Having buried my mother last week after seeing her go through progressively worse interventions due to complications from her pneumonia, I can only say that I wish more people would ask this question. Any Christianity that ignores the question of suffering neither addresses the reality of the Sin nor the biblical witness.
The question of suffering is central to Scripture. It is both a sign of God at work in us for our edification, and a result of the Fall.
But most importantly, and I say this with all sincerity, it is a light and transitory thing.
Paul says in Romans 8:

18 I consider that our present sufferings are not worth comparing with the glory that will be revealed in us.

He goes on to say:

19 For the creation waits in eager expectation for the children of God to be revealed. 20 For the creation was subjected to frustration, not by its own choice, but by the will of the one who subjected it, in hope 21 that[h] the creation itself will be liberated from its bondage to decay and brought into the freedom and glory of the children of God.

This is a substantial claim to @MasonWheeler's answer that death is preparation for the next.
The concept that this world is bent and fallen is pretty standard in just about every form of Christianity.  That this world is not what God intended it to be is the starting port. But the hope of the Gospel is that this suffering is not the end.
That &quot;death is swallowed up in victory&quot; is central to our hope.  If, as Paul points out, there is no resurrection, then we above all men are most to be to be pitied.  Without the resurrection, then indeed, such suffering would be pointless.
Paul continues, pointing out:

24 For in this hope we were saved. But hope that is seen is no hope at all. Who hopes for what they already have? 25 But if we hope for what we do not yet have, we wait for it patiently.
26 In the same way, the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us through wordless groans. 27 And he who searches our hearts knows the mind of the Spirit, because the Spirit intercedes for God’s people in accordance with the will of God.

Thus, we see that all suffering produces:

Hope (a theme picked up from Romans 5) and
A Dependence on the Spirit (and this is a good thing)

Thus, Paul can with no guile say:

And we know that in all things God works for the good of those who love him, who[i] have been called according to his purpose. 29 For those God foreknew he also predestined to be conformed to the image of his Son, that he might be the firstborn among many brothers and sisters. 30 And those he predestined, he also called; those he called, he also justified; those he justified, he also glorified.

This suffering conforms and shapes us.  It justifies us, and it glorifies.
Finally, as Christians, we know that this life is simply preparation for God's glory. If it were not, Paul could not say

Neither death nor life, neither angels nor demons, neither the present nor the future, nor any powers, 39 neither height nor depth, nor anything else in all creation, will be able to separate us from the love of God that is in Christ Jesus our Lord.

If death were the end, then death could separate us from the love of God.  But it doesn't.  It just brings us closer to Him in the end.