1. Maybe you have to eat from KGE before the immortalizing effects of the Tree of Life will work. You have to know good and evil before you can be immortal. So they had been eating from it all along, but it had no effect.
this could be, many stories from the area seem to indicate the importance of knowledge being part of being a god, so this maybe why god didn't want them to eat from it
2. Maybe they were working their way around the garden slowly and hadn't gotten to it yet, not knowing of its importance.
i think that they may have not known what the tree of life was at all
3. Maybe the Tree of Life had fruit that didn't look very appetizing, and they passed it by.
not sure since the story is very undetailed
i think one of the problems is the way the translators setup how to read it, since hebrew doesn't really have line-breaks many of the things we think would be the end of the story arn't really
look at the begining of genesis 2 as jar has pointed out its part of genesis one, the translaters did this on purpose to link the two stories together
even the last line before adam and eve are removed from eden shows that someone didn't do a good job editing it
And the LORD God said, Behold, the man is become as one of us, to know good and evil: and now, lest he put forth his hand, and take also of the tree of life, and eat, and live for ever:
Therefore the LORD God sent him forth from the garden of Eden, to till the ground from whence he was taken.
the way its edited makes it harder to figure out how the story is suppose to flow, though i have read that many critics think that someone hacked something out
of course 3:23 is to explain why man isn't in eden and 3:24 is why he can't get back in
So he drove out the man; and he placed at the east of the garden of Eden Cherubims, and a flaming sword which turned every way, to keep the way of the tree of life.
if you read this, why does god put angels in the garden? to guard the tree of life. why? because god did not want man to become like god, immortal
thats why they were kicked from eden, god didn't want adam and eve to get a shot at the tree of life and to be immortal.
knowing something means you might act on it