I certainly hope you won't give up praying for your cousin. Occasionally, I receive letters from people who've prayed for someone (such as their spouse) for many, many years -- and finally their prayers were answered. God's timing isn't necessarily ours!
Does God ever give up on someone? We don't always know what God is doing in someone's life -- His ways are often hidden from us. But we do know this: When someone truly turns to God -- even after years of rebellion -- God always forgives them and welcomes them into His family. I'm sure the prodigal son's father must have wondered if his rebellious son would ever return, but he kept watching, and one day his concern was rewarded. The Bible says, "But while he was still a long way off, his father saw him and... ran to his son" (Luke 15:20). No matter how rebellious we've been, God yearns to welcome us home.
At the same time, the Bible solemnly warns us not to assume we can leave our repentance to the last minute. The more we resist God, the easier it becomes to keep on resisting Him -- until suddenly it is too late. The Bible warns, "Disaster will overtake him in an instant; he will suddenly be destroyed -- without remedy" (Proverbs 6:15).
Continue praying for your cousin, that God will convict him of his sin and his need for Christ. In addition, ask God to give you opportunities to express your concern to him, and to urge him to give his life to Christ.