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Objection: Elisha did miracles, yet died of an illness
"Now Elisha was fallen sick of the sickness whereof he died..." -- 2 Kings 13:14.
Let's do a little Bible arithmetic. (If you hate math, feel free to skip this paragraph.) Elisha was called during the reign of Ahab. Let's assume that he was 20 years old at the time; he was obviously grown up already. Ahab ruled for 22 years (1 Kings 16:19). We know that Elisha's call could not have been closer than 3 years to either end of his reign because of the drought before Elisha's call and the three warless years after it. Assume for the sake of argument that Elisha was called in the 11th year of his reign (we'll split the difference). Ahab's son Ahaziah replaced him and reigned for 2 years (1 Kings 22:51). Jehoram succeeded Ahaziah and reigned for 12 years (2 Kings 3:1). His replacement, Jehu, reigned for 28 years (2 Kings 10:36). His replacement, Jehoahaz, reigned for 17 years (2 Kings 13:1). His replacement, Jehoash, reigned for 16 years. Elisha talked with Jehoash, so he was still alive then. If we split this down the middle and assume that this talk happened in the eighth year, we would estimate Elisha's age at his death as 20+11+2+12+28+17+8 years. Just so that you don't have to activate the Windows calculator, that adds up to 98 years old, assuming that he died fairly soon after he got sick. For that time, that was a stupendously long life. Perhaps if you dig a little deeper than I did, you could narrow down Elisha's age a little bit more. Let's compute the bare minimum. Say that he was 15 years old when he was called, and that he was called 3 years from the end of Ahab's reign, and that he and Jehoash talked right after he became king. He age at death would still be 15+3+11+2+12+28+17+0 years, or 88. That is the minimum.
So Elisha outlived his contemporaries and had to be 90-ish when he died. That's not bad!
It is unscholarly to claim that Elisha's illness proves that healing is not available to all. Elisha indeed died of an illness even though he was used to bring healing to others. What does this prove? If you look at Elisha's life, it proves that obedience will keep you alive a good long time!
At this point, Elisha may simply have wanted to go on to his reward rather than be healed. When you get to be that age, you don't have to stay here if you don't want to. You can believe for healing, but someone who is ready to die may not have much incentive to do so. Elisha was certainly old enough to have a right to do that without it being a blemish on healing ministry. If anything, we can prove that Elisha got to reap what he sowed in terms of health in his body.
There is no record that Elisha asked to be healed. Therefore, you cannot use Elisha to "prove" that God may refuse a request for healing! To prove that, you would have to come up with a couple of cases in the Bible where someone actually asked God for healing and was denied. Have fun looking.
In fact, let's turn this objection on its head. Elisha lived with such an anointing in him that a man was raised from the dead when his body touched Elisha's bones after he died. Therefore, this anointing was in him throughout his life after Elijah was taken up. This makes a good case for the statement that the anointing lengthens your life!
It is true that some ministers who held healing crusades have died of illnesses before their time. That was not God's will, but it has happened. This does not prove that the message they preach was untrue, any more than the gospel is untrue just because some famous preacher shacks up with his girlfriend. As repeatedly stated here, you get doctrine from the Word, not people's experiences!