This is true, but misleading. In the cases of 1976 and 1980, it confuses the cause and the effect. Gerald Ford ('76) and Jimmy Carter ('80) were challenged from within their party precisely because they were weak incumbents who looked likely to lose in the fall. Conversely, Reagan was highly popular in 1984 and had a strong economy backing him up. Does anyone seriously think that Mondale would have beat Reagan if Gary Hart hadn't challenged him for the nomination?
In three similar scenarios at national conventions in the past 35 years, when there have been large splits within one party during the convention itself, the candidate ultimately didn't win the general election.
In 1976, Ronald Reagan challenged Gerald Ford's nomination at the Republican National Convention in Kansas City, Mo. Jimmy Carter won that year.
In 1980, Sen. Edward Kennedy challenged Carter's nomination — and Reagan won. And in 1984, 1,200 delegates voted for Sen. Gary Hart on the convention floor rather than Walter Mondale. Reagan won again.
It is certainly possible that appearances at the convention could hurt Obama. If a bunch of Clinton delegates are photographed scowling after the vote and sitting on their hands during Obama's speech, that would hurt. But this event could also work to the Democrats' advantage if it shows delegates literally in the act of overcoming their differences and rallying behind the nominee.