Genesis 3:23

"So the Lord God banished him from the Garden of Eden to work the ground from which he had been taken."  Genesis 3:23

The Qbible has the word for banished translated as "sent away from."  So that man would not eat from the tree of life he was sent away from the Garden of Eden where it grew. 

A quick internet search will pull up several various reasons that God would take away the tree of life after Adam and Eve ate of the tree of knowledge of good and evil, including fear that man would become competition and just the simple explanation that God couldn't let them eat from the tree because it would thwart their punishment.  Several different sites suggest if man lived forever with his capacity for evil, Eden would become a hell on earth.  Whatever the reason, the Bible doesn't expound upon it here in Genesis 3 - it only tells us that it was because man ate from the tree of knowledge and became like God - knowing good and evil.

Let Us Reason Ministries reasons that banishing Adam and Eve from the garden was not just an act of justice, but of mercy also.  "For them to continue to live in the sight of the tree that made them fall and the one that would give them life would be a constant reminder of their disobedience."

Even though I am trying to do this study in order, I do think it is important to know that we have been given a way to access the tree of life again.  Revelation 2:7 states that the tree of life is in the paradise of God and the right to eat of it will be given to the victorious that hear and listen to the Spirit of God.  Revelation 22 tells us that the people of Jesus Christ will be given the right to eat of the tree.  So to gain eternal life we must follow Christ.