The statement Hebrew 9,27: Just as man is destined to die once, and after that to face judgement ..., is clear. There is no room in the bible for a being born again and again according to the far-east doctrine of Karma.
Where ever you find something about born again in the bible, God speaks about being born again to a new life trough his Holy Spirit as a disciple of Jesus. (John 3,5: Jesus answered, "I tell you the truth, no-one can enter the kingdom of God unless he is born of water and the Spirit.) This offer is for everybody of us from God trough his son Jesus Christ: John 11,25: Jesus said, "I am the resurrection and the life. He who believes in me will live, even though he dies.
The resurrection at the end of times with a new body, which will never die again, is a single event. It has nothing in common with transmigration of souls.
Matthew 17,10-13
The disciples asked him, "Why
then do the teachers of the law say that Elijah must come first?"
Jesus replied, "To be sure, Elijah comes and will restore all
things. But I tell you, Elijah has already come, and they did not
recognise him, but have done to him everything they wished. In the
same way the Son of Man is going to suffer at their hands." Then
the disciples understood that he was talking to them about John the
Baptist.
This passage is sometimes understood as proof for reincarnation, but Jesus speaks in this context of the task, to prepare the people for the coming of the Messiah in the way of Elijah (Malachi 4,5-6). This task did John the Baptist fulfil, but he was not a reincarnation of Elijah.
Luzius Schneider 18. June 1999