Firstly, I never said God does not heal. My stance is that God does not always heal. The two are very significantly different.
As to why God might not heal, how about "My grace is sufficient for you, for my power is made perfect in weakness"? (2Co 12:9) - if Paul could boast in his infirmities (the ones that obviously hadn't been healed), maybe we could too.
Here's the thing. We clearly have a conflict between the "healing in the atonement" teaching (that God always heals) and life around us that makes it very clear God does not always heal. One way or another things have to resolve. Either Scripture is wrong, or our interpretation is wrong, or there's some other reason why God isn't healing in ways we might expect. To resolve the conflict we need to figure out whether there are other ways the text can be interpreted (without butchering the context, or twisting things to suit our preferred interpretation) or if there's something about the church today that hinders things (e.g. if my life is riddled with unconfessed sin I shouldn't be surprised if God doesn't work powerfully through me)
There's one line of thought out there that essentially goes along the lines of "sickness doesn't exist in heaven and therefore has no place on earth", which sounds very appealing but this argument collapses when drawn out even a little. There's no death in heaven either but death clearly does exist on earth, not least because God decreed it would be so after Adam and Eve ate the forbidden fruit. Until the new heaven and the new earth are with us we will continue to experience death, sorrow and pain so unless we want to say we will achieve blissful immortality this side of heaven it seems odd to pull sickness out of the mix in isolation.
A verse often used by people who support the "God always heals" teaching is Ps 103:3. But looking at the overall context of this verse doesn't support the meaning that so many people assign to it, even though on the face of it the meaning appears obvious.
David was righteous aside from his one issue with Bathsheba and Uriah the Hittite (and 1Ki 15:5 puts this in black and white), so the only recorded iniquity he committed related to Uriah. God had forgiven him following his repentance after being challenged by Nathan, but the child Bathsheba bore for him died. Looking at 2Sa 12 we see David told that the Lord had put away his sin and he would not die, and on hearing his child would die David pleaded with God and fasted for a week but the child still died. Then when the child died David washed, anointed himself, and worshiped God on the basis that while the child lived he fasted and wept because God may have saved the child but now the child was dead he couldn't be brought back. If David knew that God forgave all his sins he must have written the psalm after the incident with Uriah, in which case he would also have known that God did not heal all our diseases in the physical world because he had watched his son die.
From that it seems more likely that "God who forgives all your iniquities and heals all your diseases" refers to healing in the form of being given a perfected body in the afterlife rather than necessarily physical healing in this life, given that David's son quite demonstrably wasn't healed of his diseases in this life. This ties in with Romans 8:23 referring to how we are "eagerly waiting for the adoption, the redemption of our body" and the future promise of a new heaven and new earth where there is no more sickness, no more death, no more sorrow, no more pain. I'm still seeing this as representing a promise of future perfection rather than any guarantee of physical healing in this life, which also ties in with what Jesus said about how we must deny ourselves, take up our cross, and follow Him.
Rolling forward to New Testament times and it's clear that Jesus healed a lot of people but even there it seems presumptuous to assume that sickness and infirmity will always be healed. I realise there are a few conflicting interpretations of just what Paul was referring to as the "thorn in the flesh" given to him but even putting that one aside we see him telling Timothy to "use a little wine for your stomach's sake and your frequent infirmities" (1Ti 5:23, NKJV) so it seems even back in the days of the early church there were people who weren't healed of their infirmities.
One of the books I've been reading lately (I forget which one offhand, there have been a few) raised the question whether we would be willing to give up everything in this world to follow Jesus if all we got out of the arrangement was Jesus Christ and nothing more. It's something I find very challenging - the question of whether I'd give up worldly wealth, my health, my physical well-being, whatever social and financial status I may have, all in exchange for the kingdom of heaven. But that seems to be just what Jesus is describing when he used the analogies of the "pearl of great price" and the "treasure in the field" that caused the man to sell all that he had to acquire it. What Jesus said about "if your eye causes you to sin" seems to reinforce this, that it's better to be physically imperfect and get into heaven than be physically intact but sinful. Where is the cost in plucking out our eye or cutting off our hand, if we are all but guaranteed a replacement just by asking for it? What use is a healthy body if our spirit is dull?
I often wonder whether I could follow in the footsteps of Job and honestly say "Naked I came from my mother's womb, naked I shall return... blessed be the name of the Lord". But I fear if we focus too much on the "what's in it for me" question when it comes to following Jesus we end up following on our terms rather than His, and become customers rather than disciples. The teaching that as Christians we are assured perfect health flies in the face of "take up your cross and follow me" and turns our Christian walk into a list of things we assume we're going to get. What we're going to get is a place in heaven and no guarantees whether we'll be rich or poor, sick or healthy, popular or despised, in this world. We must be ready to give up all that we have in this world for the sake of the cross, whether that relates to financial prosperity, social status, good health, whatever. If there's anything we have that we would not be willing to leave behind if Jesus called us away from it, we aren't following Jesus.
but much sowing done . 4 others baptised .. demons manifested and casts out . another day in the life .. 
