Since several comments have mentioned Dukakis in the tank and Nixon sweating: Political scientists are generally skeptical that gaffes impact the outcomes of presidential elections. See for instance political scientists Brendan Nyhan and John Sides. I'm not aware of any political science study that showed that a gaffe in a presidential election had a discernible impact on the eventual outcome. Presidential elections are primarily decided by the state of the economy. Additional important factors may be whether the country is at war, how long the president’s party has held the office, and which candidate is more ideologically moderate (Gelman and King, 1993, Vavreck, 2009, Hibbs, 2000, Bartels and Zaller, 2001). So I don't think the mentions of Nixon and Dukakis can count as examples of campaigns tanking due to gaffes. A 2003 experimental study found that watching the Nixon-JFK debate on TV led to a more favorable evaluation of JFK but we can't tell from that whether it had a profound enough impact on voters in 1960 to actually affect the election.

These "fundamentals" don't matter as much in primaries though. Gaffes may signal unpreparedness to other party elites and lead to negative media coverage (which turns both voters and elites temporarily away from a candidate).