They never ate from the tree of life. The Wholly Babble says J E Hoover - plus unnamed friend as he says "we"- put the angel guards at the entrance to the garden so as to stop the naughty couple from eating from the tree of life and "living to time indefinite".
But why didn't Adam eat it earlier? There was no restriction about it!
Oh wait! Let me see...
Eve: So, Adam, God said we were not to eat of just the tree of knowledge of good and bad, correct?
Adam: Yep, pretty sure about that now. Well, He's been goin' on about it for 30 years, so I'm pretty sure that's it.
Eve: (sigh!) Ok, and there is no restriction on eating from the tree of life?
Adam: Correct again! You're real quick Eve! Took me ages to get that!
Eve: (bigger sigh) Ok, never mind. Now listen, God is trying to tell us something. We are SUPPOSED to eat from the tree of life!
Adam: Wow! That never occured to me!
Eve: Why am I not surprised!
Adam: Errr... what?
Eve: Never mind. Just tell me which tree is which.
Adam: Errr... eenie meenie... THAT ONE!