I hope you won't stop praying for your cousin, because only God can break through the hard shell he has built up around his heart. And repeatedly I have seen God do exactly that, in response to the prayers of His people. Remember Jesus' words: "With man this is impossible, but not with God; all things are possible with God" (Mark 10:27).
Remember, too, that God is willing to forgive anyone who truly turns to Him in faith and trusts Christ for his or her salvation. Just as the father in Jesus' parable of the prodigal son ran out to welcome him when he returned home, so God joyfully welcomes us when we turn to Him - even at the last minute. The Bible tells us that there is "rejoicing in heaven over one sinner who repents" (Luke 15:7).
At the same time, the Bible solemnly warns us against repeatedly turning our backs on Christ. The reason is because as time goes on, our hearts become increasingly hardened and calloused - even to the point that we can no longer hear God's voice calling us to repentance. The Bible warns, "My Spirit will not contend with man forever" (Genesis 6:3).
If God gives you the opportunity, ask your cousin what keeps him from God. It may be pride; it may a particular sin; it may be fear. But let him know you love him - and so does Christ.