In 1956 President Eisenhower decided not to run because of bad health.In this timeline Nixon is elected president. Would Kennedy play it safe and sit out 1960??
Probably would depend on how things were going. How has the more hawkish Nixon responded to things like Castro gaining power in Cuba? How is the economy doing? Those are likely to be the decisive factors in whether the Democrats think they can win or not. Which would probably be what decides Kennedy and others whether to stand or not.