Vice President Gore was disgusted by Clinton's behavior with Lewinksy Lewinsky, his mistress.
Was he really? I know that he avoided campaigning with Clinton during the (earlier part of the) election cycle in order to eschew the embarrassment caused for the administration by the Lewinsky Scandal, but did he actually have any personally moral objections to the scandal substantial enough to stop him from running with Bill in a hypothetical third term.
Then again, I can imagine him declining to run (and perhaps even feigning disgust with the scandal) if he thought that decision would best secure his own future political career and chances of becoming president.