Well, Chakotay was a very life like and fringe type character in Caretaker. When I watched that episode for the first time, I thought he'd be my favorite character even with the dreadful Indian cliches that episode alone harped at us.
Really the main reason I think Chakotay got relegated out of the spotlight was Janeway. When Jeri Taylor was around, Janeway was hogging the spotlight to put it lightly and everyone else was put on the back burner accordingly. So for the first three years he really was just a sounding board for Janeway's ideas and the guy carrying out her orders. By Season 4, even when Ryan was out of the picture and Janeway was only -a- main character instead of -the- main character, Seven was centered heavily in a lot of episodes as if to compensate for her not being there before and by this point the Doctor was getting more and more episodes since he pretty much was the popular character.
So Chakotay was always there, he was probably doing something important but.. he wasn't interesting enough to capture the attention or likability of the audience and not given enough screen time to repair this damage. Throw in the facepalmingly bad Indian cliches and tribal stories, coupled with Beltran's often lackluster performance and well... yeah.
Really Scorpion was the only other episode Chakotay reached his potential as a character. There he was his own man, standing up to the captain and you see a true difference of opinions and a bit of drama that we were promised with the premise. He could've been a lot more, but really wasn't sadly. Just the captain's yes-man. I've joked more than once that after Caretaker, Janeway had him castrated.
It could well be that part of Chakotay's lack of prominence was just due to the non-use of the whole Maquis storyline as well. Another missed opportunity.