I have wondered whether Rehnquist's refusal to resign was not to help Bush politically, rather to provoke other tired old justices into retiring with less guilt about giving up their seat to a conservative. (In other words, he was faking his intention to get past the Bush presidency...)
or it may have been personal, at that point it is hard for almost all of us to actually know what we do (any FR posters who are from death are VERY welcome to give perspective on this! How one thinks when the facts are at hand is a big deal to almost anyone's imagination.)