No, God hasn't given up on your brother, and perhaps his sickness will finally make him face his spiritual condition and cause him to turn to Christ. The Bible says that God "is patient with you, not wanting anyone to perish but everyone to come to repentance" (2 Peter 3:9).
Even at the last minute, God can touch someone's heart and they will respond, after a lifetime of living without Him. Recently, I heard about a man who was trapped under an overturned bulldozer. A bystander told him about Christ, and minutes later he died with a smile on his face, because he had finally given his life to Jesus and knew he was going to heaven.
I think also of the two criminals who were crucified with Jesus. One mocked Jesus and refused to believe -- but the other turned to Jesus in faith, and received Jesus' promise of Heaven (see Luke 23:39-43).
Pray for your brother, and pray too for the right words to say to him. Avoid harshness or a judgmental attitude; simply tell him that God loves him (as do you), and Christ died to make it possible for him to go to heaven. Be prepared also to read a Bible verse to him (such as John 3:16). He may react negatively -- but even if he does, you'll never regret telling him the most important news anyone can ever hear.