Prayer is one of those "I want it, I want it, I want it, maybe not" phenomena. I'm not thinking so much "be careful what you ask for." Rather, I'm thinking about rolling with the plan and purpose of God.
Think about it. What if the illness that we're asking God to heal is given by God for spiritual growth in Christ? Would we really want to deprive that person or ourselves, for that matter, of blessing?
There are those who say God doesn't bring about financial ruin or car accidents. But that view does not comport with God's revelation of Himself in His Word, how He wants us to understand Him. Just look at Lamentations, chapter 3 and see Jeremiah's clear understanding of the hand of God behind the horrors experienced by His people. Yet amidst those horrors sounds the redemptive heart of God that fuels hope: "The steadfast love of the Lord never ceases; His mercies never come to an end; they are new every morning; great is Your faithfulness." (Lam. 3:22f.)
This bigger view of life with God calls for circumspection in prayer. Nothing wrong with praying for relief or well-being. Jesus did it. "Father, take this cup from me." But the governor for His prayer was, "not My will but Your will be done." Paul took the same tact when asking to be relieved of his thorn in the flesh in 2 Cor. 12.
I guess the best way to put it is that when we cast our desires of prayer on the waters of God's will, we don't want to have a string attached to yank it back. We want it, we want it, we want it, but maybe not--and that's okay. In fact, that is ultimately what we really want, that the will of our all wise, sovereign Father in heaven would be done in all things.