I don't think either of the two posts thus far adequately addresses the issue of the miracle of healing. Both answers seem simplistic and do not take into account the full teaching of God's Word.
The issue certainly is not about "cheating death" completely. The Word says we will all die -- but even with that text there is the ambiguity of what about those believers alive when Jesus comes.
The issue of God's sovereignty is certainly something to be considered. Yet, there is some ambiguity here also because the Scripture mentioned several times that God changed His mind in response to prayer. Scholars and skeptics dance around the clear language of Scripture to try to erase the ambiguity, but the answers are usually quite inadequate.
The clear teaching in Scripture in not a few places is that some people do not die when it appears they most surely will as a direct result of prayer. It is the miracle of healing. Sure, as Tony points out, such divine intervention is rare -- I think that is why it is called a miracle. However, Tony's statistics are somewhat skewed because the Bible says directly that not everything the Lord did has been recorded. Therefore, it is impossible to know exactly what the statistical ratio of people healed to people who were not healed truly is.
As a Baptist I'm often at odds with some of my brethren because I believe strongly in the gift of healing. The fact that the majority of people that I've prayed for have not received a miraculous healing (save that which comes by way of translation from this life) does not discount those who were healed contrary to all human expectations. Nor does the fact that God sometimes (or as Tony points out many times) answer "no," destroy my belief in the power and providence of God to send any miracle any time He chooses.
I've seen life support removed and the person die. I've seen life support removed and the person live. I do believe that whether we live or die, it is a matter of God's power and providence ultimately. A couple of times I have watched a person remarkably and unexplainably rise from a bed of death. When that happens, one's faith in God is greatly impacted.
While I don't understand all of the how and why of healing nor the importance of statistical data, I do trust the straight-forward teaching of the Bible in both testaments that demonstrate God's power over death and life.