It wasn't punishment that drove Adam and Eve from the garden it was mercy. If they would have eaten from the tree of life they would have lived for ever in their fallen state. There would have been no hope for them. We can eat from the tree of life anytime we want when we get to heaven.
Revelation 22:1-5 (NASB) " Then he showed me a river of the water of life, clear as crystal, coming from the throne of God and of the Lamb, in the middle of its street. On either side of the river was the tree of life, bearing twelve kinds of fruit, yielding its fruit every month; and the leaves of the tree were for the healing of the nations. There will no longer be any curse; and the throne of God and of the Lamb will be in it, and His bond-servants will serve Him; they will see His face, and His name will be on their foreheads. And there will no longer be any night; and they will not have need of the light of a lamp nor the light of the sun, because the Lord God will illumine them; and they will reign forever and ever."