The power of an incumbent president running for reelection may be such that it is impossible to defeat him in all but the most extraordinary circumstances. In the elections since 1945 Truman, Eisenhower, Johnson, Nixon, Reagan, and Clinton all won reelection, usually by a substantial margin. Only twice, 1980 and 1992, was the incumbent defeated (not counting 1976 since Ford was never elected in the first place).
1980 - Carter loses his reelection bid. Three factors lead to the loss.
1) The economy. It was so bad in so many ways that they had to invent a new word for it (stagflation anyone?). Interest rates, inflation, unemployment. There was simply no good economic news in the late 70s.
2) An unprecedented overseas crisis. The Iranian revolution, the hostages, the failed rescue attempt. They invented a TV show (Nightline) just to cover this one mega-story of American helplessness and victimization. Add to this the Soviet invasion of Afghanistan, Carter's less-than confidence inspiring response of boycotting the Moscow Olympics and again, bad news all around.
3) An opponent with rare communication skills and charisma, Ronald Reagan.
If any of these three factors had been different, Carter could have won reelection.
1992 – Bush Sr loses his reelection bid. Again, a trifecta lead to the loss.
1) The economy. While not nearly as horrible as it was in the late 70s, the recession of 90-91 came at the end of a decade of growth. People were accustomed to a more or less positive economic environment and they were shocked by the downturn. Add to this increasing nervousness over competition from Japan and the relative economic picture was not pretty.
2) An unprecedented third-party candidate. We tend to forget now that for a while in early summer Ross Perot lead in the polls. People were genuinely enthusiastic. Then he went flaky and dropped out. Then he dropped back in and still finished with 19 million votes.
3) An opponent with rare communication skills and charisma, Bill Clinton.
If any of these three factors had been different, Bush Sr could have won reelection.
Looking at 2004 one sees possibly two of these factors. The economy is stable with signs of growth but enough people feel enough anxiety that the opposition could exploit the situation to his advantage. The war is unpopular or at least enough people are ambivalent about it and open to ideas by the opposition. The third key factor is missing: the opponent with rare communication skills and charisma. (Kerry actually has a kind of negative charisma and a bizarre communication style where the more he says, the less people understand.) Without that, history tells us that the incumbent president, wielding the power of the office and relying on the inertia of the American electorate, will win.