Rumsfield had to go, the Rats would have made his life hell for two years. I would not at all be surprised to learn Rumsfield insisted Bush accept his resigation this time. Bush did not dump him, he just had to go, too many enemies and not enough friends.
Relative to other Presidents, Bush has had relatively little turnover during his 6 years in office. People always leave the last two years of the second term to get a jump on opportunities in the private sector or in academia.