I suspect you keep praying for him because you love him, and you care deeply about what will happen to his soul. You also know he's missing out on life's greatest joy, which comes from walking every day with Christ in our hearts.
When we pray, we need to remember that God's ways and God's timing aren't always the same as ours. Don't stop praying for your brother. Almost every week I get at least one letter from someone who's been praying for years for someone who doesn't know Christ–a spouse, a relative, a friend. In many cases, the person prayed for has eventually turned to Christ, and their life has been changed. What if they had stopped praying?
Remember, God is able to do what we can't do. Only He can convict your brother of his sins, and only He can convince Him of the truth of the Gospel. That's why no one is hopeless, for God can break through even the hardest heart. The Bible says, "Is not my word ... like a hammer that breaks a rock in pieces?" (Jeremiah 23:29).
Do not only pray for your brother, however. As God gives you opportunity, also speak to him about your concern for his spiritual condition. The Bible says, "Always be prepared to give an answer to everyone who asks you to give the reason for the hope that you have ... with gentleness and respect" (1 Peter 3:15).