Does God desire that each of us be physically healed? Our loving God doesn't want any of His children to be burdened with pain. So in that sense, yes! God also desires that everyone will be saved (1 Timothy 2:4); but in reality, that won't happen (John 14:6). Not all of what God wants will necessarily come to pass — including healing.
There are many biblical examples where people are not physically healed. Paul mentions his own “thorn in the flesh” (2 Corinthians 12:7) which God didn't cure, even after he prayed three times for healing. Timothy is said to have had “frequent illnesses” (1 Timothy 5:23), and rather than asking for Timothy to be healed, Paul instructed Timothy to “use a little wine” to help with his condition.
Elsewhere, Paul notes that he left Trophimus sick in Miletus (2 Timothy 4:20). And Jesus, in John 5, healed one man by the pool of Bethesda, even though there were many others who were sick.
Even some of the most faithful Christians won't be healed, at least not until Jesus comes again. This is demonstrated in Scripture and confirmed by our own experience.
One reason that God may choose not to heal (though it's not the only reason) is expressly stated by Jesus in John 9. Regarding the man who had been blind from birth, Jesus plainly states the reason for the man's condition: “This happened so that the work of God might be displayed in his life” (John 9:3). Greater good may come from an illness than would have resulted from God’s divine healing.
Anytime there's a situation where healing doesn't come, we need to remember that healing isn't only a theological issue — it's also an intensely personal one. We may never fully understand why God heals one person and doesn't heal another. Ultimately, the choice is entirely up to God. His divine will has a purpose, which is more amazing than we will ever be able to fully comprehend. We need to try to trust in the God who has demonstrated Himself to be trustworthy, and to remember the love that God has shown us.
Be encouraged by Paul’s words to the church at Ephesus:
"I pray that out of his glorious riches he may strengthen you with power through his Spirit in your inner being, so that Christ may dwell in your hearts through faith. And I pray that you, being rooted and established in love, may have power, together with all the saints, to grasp how wide and long and high and deep is the love of Christ, and to know this love that surpasses knowledge — that you may be filled to the measure of all the fullness of God" (Ephesians 3:16-19)."