By 1992, Dan Quayle was a much better campaigner and debater. He held his own against Gore in the 1992 Veep debate. So, I wouldn't count Quayle out in 1996 if he had served 2 full terms as Vice-President and the economy was doing well.
In OTL, Dole won because he was next in line and the competiton was weak. Remember, after he won the Iowa caucuses, Dole's main competition was the controversial Pat Buchanan (fmr Nixon and Reagn press secretary and pundit) and Steve Forbes (fmr Reagan appointee to radio Free Europe/Radio Liberty and magazine publishing heir).