The apostle Paul was a man who could have concluded that God doesn't listen to people. After all, he urgently pleaded with God to intervene for him in a chronic trial. But God refused to grant Paul's request.
Does this mean Paul lacked faith? Of course not. However, there is a deeper lesson for us in Paul's life of living faith.
When Paul pleaded with God
Notice Paul's account of this trial: "There was given me a thorn in my flesh, a messenger of Satan, to torment me. Three times I pleaded with the Lord to take it away from me" (2 Corinthians 12:7-8 2 Corinthians 12:7-8  And lest I should be exalted above measure through the abundance of the revelations, there was given to me a thorn in the flesh, the messenger of Satan to buffet me, lest I should be exalted above measure.
 For this thing I sought the Lord thrice, that it might depart from me.
American King James Version×, New International Version).
What was this trial that tormented Paul? Comments in Paul's writings hint it may have been a problem with his eyes (Galatians 4:13-15 Galatians 4:13-15  You know how through infirmity of the flesh I preached the gospel to you at the first.
 And my temptation which was in my flesh you despised not, nor rejected; but received me as an angel of God, even as Christ Jesus.
 Where is then the blessedness you spoke of? for I bear you record, that, if it had been possible, you would have plucked out your own eyes, and have given them to me.
American King James Version×; Galatians 6:11).
The implication is that Paul fervently asked God to deliver him from the trial, no doubt with fasting and heartfelt prayer (2 Corinthians 11:27 2 Corinthians 11:27In weariness and painfulness, in watchings often, in hunger and thirst, in fastings often, in cold and nakedness.
American King James Version×). He wanted this hindrance removed so he could continue to spread the gospel effectively and care for the congregations God had raised up.
God's answer to Paul
Paul could have concluded that God had not heard his pleas. But this is not the case. God simply gave Paul a different answer: "My grace is sufficient for you, for My strength is made perfect in weakness" (2 Corinthians 12:9 2 Corinthians 12:9And he said to me, My grace is sufficient for you: for my strength is made perfect in weakness. Most gladly therefore will I rather glory in my infirmities, that the power of Christ may rest on me.
American King James Version×).
Whether God directly spoke these words to Paul or whether Paul gradually came to this understanding of God's will isn't clear from the Greek wording. What is clear is that Paul came to a deeper spiritual understanding that strengthened his faith and commitment.
Paul came to see that the credit belonged to God and Jesus Christ rather than to himself and that his weakness drew him closer to that source of power and strength. "I am therefore happy to boast of my weaknesses, because then the power of Christ will rest upon me. So I am content with a life of weakness, insult, hardship, persecution, and distress, all for Christ's sake; for when I am weak, then I am strong" (1 Corinthians 12:9-10 1 Corinthians 12:9-10  To another faith by the same Spirit; to another the gifts of healing by the same Spirit;
 To another the working of miracles; to another prophecy; to another discerning of spirits; to another divers kinds of tongues; to another the interpretation of tongues:
American King James Version×, Revised English Bible).
Of course, Paul's experiences were not typical of what most modern Christians experience today. Along with his great trials, he also witnessed great miracles and evidence of God's power. Still Paul's "thorn in the flesh" stands as an important spiritual lesson for us. Sometimes when we experience unanswered prayers, God's answer for us is actually "no" or "not yet." God never intended our physical bodies to last forever. He has allotted us an existence of about 70 years (Psalms 90:10 Psalms 90:10The days of our years are three score years and ten; and if by reason of strength they be fourscore years, yet is their strength labor and sorrow; for it is soon cut off, and we fly away.
American King James Version×). He is far more concerned that we develop righteous character and a trusting relationship with Him that can last for eternity. He wants to resurrect us to eternal life in a glorious, immortal spirit body not subject to weakness, illness and death (1 Corinthians 15:40-44 1 Corinthians 15:40-44  There are also celestial bodies, and bodies terrestrial: but the glory of the celestial is one, and the glory of the terrestrial is another.  There is one glory of the sun, and another glory of the moon, and another glory of the stars: for one star differs from another star in glory.  So also is the resurrection of the dead. It is sown in corruption; it is raised in incorruption:  It is sown in dishonor; it is raised in glory: it is sown in weakness; it is raised in power:  It is sown a natural body; it is raised a spiritual body. There is a natural body, and there is a spiritual body.
American King James Version×; 1 Corinthians 15:50-54 1 Corinthians 15:50-54  Now this I say, brothers, that flesh and blood cannot inherit the kingdom of God; neither does corruption inherit incorruption.  Behold, I show you a mystery; We shall not all sleep, but we shall all be changed,  In a moment, in the twinkling of an eye, at the last trump: for the trumpet shall sound, and the dead shall be raised incorruptible, and we shall be changed.  For this corruptible must put on incorruption, and this mortal must put on immortality.  So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.
American King James Version×).
In the meantime, Paul understood that God in His love will never allow us to fall into trials greater than we can endure. "But when you are tempted, he will also provide a way out so that you can stand up under it" (1 Corinthians 10:13 1 Corinthians 10:13There has no temptation taken you but such as is common to man: but God is faithful, who will not suffer you to be tempted above that you are able; but will with the temptation also make a way to escape, that you may be able to bear it.
American King James Version×, NIV). Sometimes that "way out" is simply the determination to endure the trial, to "stand up under it."
Hearing God's will
Paul was not the only one who learned that living, trusting, abiding faith is more important than physical health and long life. Even Jesus, knowing that He faced a cruel death only hours away, prayed, "O My Father, if it is possible, let this cup pass from Me" (Matthew 26:39 Matthew 26:39And he went a little farther, and fell on his face, and prayed, saying, O my Father, if it be possible, let this cup pass from me: nevertheless not as I will, but as you will.
American King James Version×). Jesus loved life and wanted to live as much as any of us. But He acknowledged a greater purpose for this physical life: "Nevertheless, not My will, but Yours, be done" (Luke 22:42 Luke 22:42Saying, Father, if you be willing, remove this cup from me: nevertheless not my will, but yours, be done.
American King James Version×).
Jesus Christ, the perfect example of faith, knew God's will was more important than His.
God knows what is best for us in the long run, even if it may conflict with our short-term wants and desires. As Peter tells us, "[cast] all your care upon Him, for He cares for you" (1 Peter 5:7 1 Peter 5:7Casting all your care on him; for he cares for you.
American King James Version×). Paul says we should be "confident of this very thing, that He who has begun a good work in you will complete it until the day of Jesus Christ" (Philippians 1:6 Philippians 1:6Being confident of this very thing, that he which has begun a good work in you will perform it until the day of Jesus Christ:
American King James Version×). Because God works within us from a broader perspective to build faith and character, He doesn't always answer our prayers in the way we desire.
Some were delivered, some not
The Bible tells us at times "women received their dead raised to life again." But "others were tortured, not accepting deliverance, that they might obtain a better resurrection. Still others had trial of mockings and scourgings, yes, and of chains and imprisonment… And all these, having obtained a good testimony through faith, did not receive the promise, God having provided something better for us, that they should not be made perfect apart from us" (Hebrews 11:35-40 Hebrews 11:35-40  Women received their dead raised to life again: and others were tortured, not accepting deliverance; that they might obtain a better resurrection:
 And others had trial of cruel mockings and scourgings, yes, moreover of bonds and imprisonment:
 They were stoned, they were sawn asunder, were tempted, were slain with the sword: they wandered about in sheepskins and goatskins; being destitute, afflicted, tormented;
 (Of whom the world was not worthy:) they wandered in deserts, and in mountains, and in dens and caves of the earth.
 And these all, having obtained a good report through faith, received not the promise:
 God having provided some better thing for us, that they without us should not be made perfect.
American King James Version×).
Even when we have unanswered prayers, know that God does listen. He does not always answer our prayers to our immediate satisfaction and instantly deliver us from our trials. But He will always do what is best for us.