I'm sure your doctor had seen similar cases in the past, and he didn't want to raise any false hopes about your brother's chances for recovery. But the human brain is marvelously complex, and I'm sure he would be the first to admit he was wrong in your brother's case.
But God was also at work, and I hope you will thank Him and give Him the glory for what happened. The Bible says God "is able to do immeasurably more than all we ask or imagine, according to his power that is at work within us" (Ephesians 3:20). One of the ways He works is through the prayers of His people, and that's one reason why we should always pray when we face hard times. The Bible says, "Trust in him at all times, O people; pour out your hearts to him, for God is our refuge" (Psalm 62:8).
Does this mean God always answers our prayers the way we want Him to? Sometimes He does–but not always. God knows what is best for us, and sometimes His answer to our prayers is "No" or "Not yet." But that shouldn't keep us from praying! God loves us, and He can be trusted to do what is best. The Bible tells us to "pray continually" (1 Thessalonians 5:17).
As a footnote, I pray your family won't forget the lessons God has been teaching you through this experience. Every day is a gift from Him, and we should use it to serve and love Him.