Why did The Giver decide to stay behind to help the community in The Giver?

I think that you can find this answer at the very end of
Chapter 20.  The Giver does not want to come with Jonas because he wants to be with his
daughter once he has finished his work.  What this means is that he wants to
die.

Since I am not him, I cannot be sure if he made the
right decision.  He must surely have been quite sad about the way things have gone in
his life.  He loved his daughter, but the society that he lived in (and that he was very
important in) caused her to die.  In that situation, you can see where he might not want
to live any longer.  He might want to destroy/remake the society (by helping Jonas) and
then go to be with his daughter.

So I guess I think he's
made the right decision.  He is sad about the past and, I think, he feels too old to
start a new life.

Looking again at your question, I think I
should talk some about why he would want to help the community.  I think it is because
he feels like he is partly responsible for how the community is.  He has all these
memories and could, presumably, have helped to change the community.  Because he didn't,
he feels responsible.  I think this is an admirable attitude on his part -- he had a
hand in causing the problems and he wants to be a big part of fixing
them.