A Refutation of Annihilationism
1) Your statement, "Mortal man lives a short time, yet people feel justified to condemn humans to eternal suffering because of the failure to grasp life while on earth," falsely presumes that God does not provide a person enough time to reach a level of complete accountability to the Truth. Upon what do you base this? Also, contained in your statement is the false assertion that eternal punishment is the consequence of a person failing to "grasp life." Most definitely Scripture makes it clear that a person, in this life, is given sufficient evidence and knowledge--as well as a measure faith--to make an informed decision for Christ. In other words, any failure on the part of a person is not the result of failing to "grasp life," rather, that person fails to receive and act upon that which enables them to "grasp life," to do something they have been enabled to do; namely, to submit to the work and righteousness of their Maker. For if they act upon what evidence/revelation that is given to them (our "moral compass," God's natural creation, and His Word--in whatever measure available), then they will be saved.
2) Eternal Hell-fire is not "the end the ultimate resolution for sinners who refuse to be healed?" (I am not positive what you mean by this.) It's the consequence of rejecting God Almighty in this life. What is being resolved if it is a resolution? A resolution of what? The problem of sin is not resolved in Hell. In Hell, sin is still imputed to the condemned.
3) I believe the evidence weighs heavily in favor of everlasting punishment in a literal Hell. If there is no such thing, then there is no consequence for rejecting God in this life. If there is not such a Hell, then what is the alternative to Universal Salvation or limited/finite punishment in Hell? That would be Annihilationism. But if Annihilationism is proposed, then where does sin go after mortal death? It cannot not be imputed to Christ on the cross. It is not relegated to some state or place of limbo. So what happens to it? If we say it is destroyed along with the person, then is that not a claim for a second means of eradicating sin along side of the Cross? Shall we dare say that through the lack of faith (rebellion of man) sin can be destroyed, just as sin is destroyed through faith in the work of a cross? Would that not be equating a lack of faith with faith? Shall we dare equate transgression with the power of the cross? I think not. If it is otherwise, then all a godless person has to do is kill themselves and their sin is then eradicated, meaning they have the power not only to escape the wrath of God, and but also to thumb their nose at God. Do proponents of Annihilationism actually believe that man has such power over God Almighty and sin?
So what if God annihilates a person/soul; the annihilated person will not exist, so he/she would not care. In Annihilationism, there is no punishment, for punishment can only be inflicted where the object of such affliction actually exists. Is a comatose prisoner in a prison aware of their punishment? No? Then what would be the point in keeping them in prison, which is a form of punishment? Would a society waste money continuing to incarcerate an inmate pertaining to whom it is known that the inmate's comatose state is absolutely permanent? So annihilation is certainly not a form of punishment, for how can a person be punished if they are not even aware of such punishment?
I conclude, therefore, that Annihilationism is not an option. So let's resign that to the abyss of ignorance where it truly belongs. As far as I know, that only leaves Universal Salvation or finite/limited punishment in Hell. However, the arguments for Universal Salvation and finite/limited punishment in Hell are full of Scriptural and logical problems. And they are certainly refutable, which, by the grace, knowledge, and power of God Almighty and His Word, I believe I can certainly do.
4) I have heard it said that God does not send people to Hell; they send themselves to Hell. There is truth to this claim with respect to its point. An apt parallel would be a person who ends up in prison as a result of wicked behavior. If we say that it is the State that has sent the person to prison, and make no mention of the responsibility the person has concerning the cause of the person being sent to prison, are we not presenting a half truth? The State does not want to send people to prison (neither does God want to send people to Hell), but it has no choice because justice requires an answer to man's wickedness and unrepentance. What would we think if our government decided it would never again send anyone to prison no matter what crimes people commit? Would we not label such a government as unjust? And is not justice one of the very attributes of God? So we can begin to see that the necessity of an eternal hell lies in part in the very nature/character of God Himself.