A lot of cessationists will argue that Isaiah 53:5 "by [Jesus'] stripes, you are healed" is referring to a spiritual healing. It can look that way at first—if you are biased against God healing people.

First, Scripture itself clarifies the issue (Matthew 8:17), when Jesus healed the sick, Matthew says this was done to fulfill Isaiah 53. Second, Michael L. Brown points out that the promises of God's healing are tied with smiting the Israelites—the key passages mention both together. So when we see that the Israelites were physically killed, scattered, and defeated, we should expect their restoration and healing to be equally physical (their hardship was not spiritual, so their healing would not be either). Third, Brown also points out the explicit reference in Isaiah 33:24, to the physical healing of Israel when they are restored.Michael L. Brown, Why I Believe in Divine Healing, 16/01/2018, ASKDrBrown, https://www.youtube.com/watch?v=9E7ihr0N-Hk

Regardless of whether you are convinced: what if Jesus died not only for our sins but also for our physical healing? Would that mean that God always wants to heal? No! It still wouldn't!

In the same way that we don't expect everyone to immediately always get saved (although we fervently go after it), so it is that we should not expect that everyone always will get healed. An excursion to how we think about salvation will help.

How our thinking about salvation can help

These same principles are relevant for salvations. We know God's general desire is that all people should be saved (1 Timothy 2:4), and that Jesus died for sinners, but we should not presume that that means that God wants to save any particular sinner (or all of them) right now. We need to follow the Spirit.

Sometimes it takes many years for people to come to God. Some even come on their death-bed. We can't force this decision onto people, and even sinners themselves can't pray a magical formula to definitively get themselves into heaven at that moment. That's because salvation is about answering God's call personally, which requires that His Spirit draw the person directly, wooing them to Himself, convicting them of their sin and their need for God. It's highly personal.

God hasn't setup a giant spiritual mechanism where you just have to say the right words "abracadabra" and you're in—yet this is how we treat it when we try to lead people to God through a "Sinner's Prayer". This is the key reason why so many people who profess to be Christian fall away so quickly: they never actually entered a relationship with Jesus in the first place! We presumed it. We never saw the Spirit in their lives: that convicting work, that change of heart, or, for some, a pouring out of God's charismatic gifts. (See series Becoming Christian for how to become a Christian.)

Evangelism without presumption

So we need to slow down and require that people surrender, like Jesus did (recall the time that he had people come up to him to follow him, and he said, pray this prayer? No, neither do I. Instead, he challenged them to give up that which was most precious to them, Luke 9:57-62). This is going to involve something different for each person: What idol does God want this person to give up? For the rich young ruler it was his riches. For the prodigal son, it was living for his own experience, his own way. For Paul, it might have been the prestigious Pharisaical position he had. For the man who wanted to bury his father, it was his family.

I believe Ray Comfort was onto something when he sees a pattern in both the Bible and in revivals, that people get convicted first of their sin, before then seeing their need for a Saviour (we're being saved from the consequences of our sin, after all). But instead of taking a scattered approach and talking about general sins, we could ask God for what is relevant for that person, and ask them about it. Are they ready to leave that life behind? It's a personal one to one connection that God is after, so you'll notice Jesus always drilled down to a specific idol relevant to each person.

Now, that's losing trust in your idol(s). Each person always trusts in something or someone (or multiple things). So that's why we must repent and believe. So Ray Comfort reminds us correctly about repenting—but then there's the belief, the trust. And this is just as crucial.

With regard to building trust towards Christ, some people say, "you can't argue people into the Kingdom". But you can! Not literally, because only God can save, but, some people are thinkers and need to understand God's Word in a way that makes intellectual sense before they are ready to trust in it. That can require intellectual argument, and sometimes lots of it. This was the case for Nabeel Qureshi, a Muslim, who benefited greatly from discussions with a Christian to remove intellectual barriers he had that prevented him from placing his trust in Jesus. But others are going to be different because God has made them different. Others need to see Christ's love in you, grace, miraculous power, or any number of other things. Maybe they could never trust the Father because they've never seen a trustworthy man. Then God may direct their path to see how Christ can be trustworthy, perhaps through the example of a Christian father who displays integrity. If that's how God will lead them, then no amount of passionate pleading will move them before that time, and no amount of miracles will move them before that time.

Bottom line: We should not presume that God will use the same way as he used yesterday to save, because it's not the technique that saves, but God. So for different people, we will need different approaches, because they have different idols, different desires, different personalities, are on different journeys, and God has different plans as to how to show himself to each person.

And healing, then? Clearly, God doesn't heal straight away or even at all sometimes. Perhaps, dare we say, most times (though some have an extraordinary gift of healing and may see healing most times). That's reality. Just like we would expect only the full number of believers to come (which is not everyone), and then to see the Second Coming of Christ, so it is that we should only expect full healing and restoration to come to the believers until that time too. For now, we will see many glimpses of that restoration, but full perfection is not to be expected right now (for why this must be, and why it makes so much sense, see series Mission of the Church).

Salvation, healings and breakthroughs of any kind come from the one God, who miraculously provides all these blessings under the same principles. In the same way that we understand that praying for healing can take a long time of concerted, consistent prayer (perhaps a few hours, perhaps a few days)—if God wants to do it—we should understand similarly that praying for salvation can take this consistent, repeated request too. This type of prayer, as opposed to the Sinner's Prayer, does not presume God is waiting on you, holding back; and, it ensures the request is personal and not formulaic. (See Becoming Christian Part 3: How should we lead people to Christ? A Once-Off Sinner’s Prayer, or a Once-Until Crying Out? The Evangelical Charismatic approach to salvation for further detail)