God alone knows why your cousin decided to go back to his old ways. He isn't unique, however; many of Jesus' followers abandoned Him because they weren't willing to give up their old ways of living. The Bible says, "From this time many of his disciples turned back and no longer followed him" (John 6:66).
I can only guess why this might have happened to your cousin. Perhaps his decision to follow Jesus wasn't really sincere, or perhaps no one encouraged him or helped him grow spiritually. Jesus once told a parable about a farmer who scattered seed in his field. (You can read it in Luke 8.) Some of the seed fell on the hard path, some fell among rocks, some fell among thorns -- and they produced nothing that lasted. But other seeds fell on fertile soil, and produced a bountiful crop. This, Jesus said, is like God's Word when it is preached, for not everyone welcomes it.
Whatever the reason, I hope you won't stop praying for your cousin. God still loves him, and Christ gave His life for him, and that will never change. God is still able to break through the hardness of his heart, convicting him of his sin and convincing him of the truth of the Gospel.
In addition, ask God to help you be a witness to him by the life you live. Do others see Christ in you -- His love, His peace, His patience, His purity? People may ignore our words, but they can't ignore our lives.