Look at how much they played that season. For example, Cal Ripken will never get tired or need to be rested, whereas someone who only had 100 at bats will get tired much more quickly.
How does fatigue carry over into the post-season? Fatigue is NOT reset when the playoffs start. Players go into the playoffs with the same fatigue level that they ended the regular season with. So, if you have a big lead going into the last couple of weeks, it would certainly help to rest your players. Also, players do rest on 'off days'. So if you sweep your first round opponent and the other series goes 5 games, your players would pick up 2 games of rest.