We do not fail in our evangelism if we faithfully tell the gospel to someone who is not subsequently converted; we fail only if we do not faithfully tell the gospel at all.

It's fine to deal with people's doubts and explain why they have good reasons to believe in Christ. But until we tell them the good news of Jesus Christ, we haven't done our job. They need a saviour that God has provided them in Christ. Once they know that, we can do as much apologetics as we need to.

If we feel that our ministry has come to an end in one place, then it seems reasonable to move on.

Keep going until you get good counsel that is persuasive for you that you should go elsewhere.

Evangelism is not simply looking at someone and saying, "Look, you have to become a Christian". Instead, an evangelist tells us the truth about who God is, and explains where we stand as a result of that. People can ignore us - indeed, they have every legal right to do so.

I heard about a pastor in a church of 5,000 people who employed two seminary students whose main responsibility was to get four new people baptized each week. When asked, "What happens if they can't meet the quota?", his response was, "Then I'll find two students who can". This man wasn't even remotely interested in true gospel preaching. He was results-driven.

Prayer is the preview of God's action.