My response is that healing never completely died out in the Church and the Gospel still needs to be preached with signs and wonders. People still get sick today and seek healing. God still heals today.
The second argument is that it is not always God's will to heal. There are a couple of responses to that. If we don't know whether or not it is God's will to heal someone (and, as I pointed out before, Jesus healed everyone who came to him in faith asking for healing), why not pray until we know God's will and then pray in accord with what we have discerned of God's will? That way we are praying in accord with God's will.
God does not "put" any sickness on us; God does not make us sick. God is all good. Jesus came that we might have life to the full, abundant life (John 10:10). Nowhere does Jesus say, "My Father gave you this sickness so that you could learn ...."
Let us pray. Father, show us your will regarding healing today. Show us what it means to have life to the full, to have abundant life.