Obviously there are many reasons why boxers fight past their "prime". Generally it happens because of 3 reasons, the money, the good old applause, or the same single mindedness that made them champ is telling him he can do again.
1) Most of the time fighters hang around too long because of the money. You have to understand coming up boxers don't make much, but when they finally do start getting decent paydays often times its later in their career. So now when they are finally starting to see some decent paydays you think they want to retire? For every Leonard or Dela Hoya there's 10,000 other fighters making peanuts. Even if the purse looks good on paper the pot is being split between promoters, managers, trainers, etc.
2) The roar of the crowd. Some fighters who are financially set can't live without the cheer from the fans and all the adulation that comes from being a prize fighter. Even Ali once said the sound of the fans chanting, "ALI, ALI" as he came into the ring is what kept bringing him back.
3) It takes a person of great self belief to become a champion in boxing. With kind of personality trait it's hard for that fighter to be truly honest with himself and say "I don't have it anymore". Even if the fighter does lose badly to lesser opposition, he may immediately say I can't do this anymore but as time goes on he'll get that itch again. Then he'll start making excuses about why he lost, bad training camp, family problems, nagging injuries, etc. The old fighter with same mentality that told he could be champ in the first place will tell him he's got enough left for one more run to the title. Unfortunately in boxing there is no barometer that can tell you don't have it anymore. This is why I say boxing is the greatest seducer of all time, you'll feel good on the bags, feel good on the mitts, feel good in sparring, but you never really know until it's too late, under the bright lights......