No, don’t give up on him; even if he’s asking questions just to keep from facing his own spiritual need, God is able to break through the hard shell he seems to have built around his heart and mind.
Do you remember Saul of Tarsus? He was convinced that Christians were not only misguided, but that their faith in Jesus was dangerous and needed to be stamped out. As a result, he violently lashed out at them and did everything he could to convince them they were wrong. Later he wrote that “(I) do not even deserve to be called an apostle, because I persecuted the church of God” (1 Corinthians 15:9).
But God intervened, dramatically convicting Saul of his sin and convincing him of the truth of the Gospel. As a result, Saul’s life was changed—and he became Paul the Apostle, whose missionary efforts touched the whole Roman Empire. No wonder Paul could say, “If anyone is in Christ, the new creation has come: The old has gone, the new is here!” (2 Corinthians 5:17).
Pray for your friend, that God will work in his heart and show him his need for Christ. Pray too that God will give you an opportunity to confront him and ask him why he seems to be pushing God away. Ask God as well to help you be a witness to him, not only by your words but by your life. He may dismiss what you say, but he can’t dismiss the reality of a Christ-like life.