Presuming Donald Trump wants to become nominated for a second time, is the Republican party obligated to let him do so? Or can they put forward alternative candidates that would potentially defeat Trump in the primaries? Is there historical precedent for a party abandoning their previously elected President at the next election?
Gerald Ford came close to losing to Ronald Reagan in the Republican Party presidential primaries of 1976. For a variety of reasons it could be argued that's not precedent, but it certainly shows a challenger can put up a fight.
So I'd conclude there is no obligation to renominate, or prohibition of alternate candidates.
The convention tally reported on Wikipedia was: Gerald Ford 1187, Ronald Reagan 1070, Elliot L. Richardson 1. In the general election, Jimmy Carter defeated Ford.
Gerald Ford's 895 day presidency was one of the shortest in US history. His decision to pardon Richard Nixon (who had appointed him vice-president) is thought to have brought his approval ratings down and make him vulnerable to criticism for covering up details of the Watergate scandal.
Is the party obligated rules-wise?
NO. The party is obligated to nominate whoever wins the nomination by the rules of RNC nominating convention - the link is to 2016 rules, but of course the voting in 2020 will be as per yet-to-be-finalized-and approved 2020 rules. As standing, the rules generally tend to nominate whoever wins the most convention delegates (including binding delegate votes in primaries/caucuses in specific states, but general voting rules are a tad bid more complicated).
Now, if they rewrite their rules to say "Trump must win" - as the rules are voted on by the convention prior to nominating vote (more specifically, a 56-member Rules Committe), that is technically possible, and would then obligate them to nominate Trump.
Is the party obligated practicality wise?
Now, let's say the party either amends the rules to exclude Trump, or, delegates somehow vote against him even if he wins the Primaries (perhaps with some rule changing involved, or just all super-delegates or whatever RNC calls them voting for someone else).
I haven't seen exact research on this but 538 has in the past mentioned that as of today, Trump seems to have enough base support in the party (30-35+% of overall population) to make this a Bad Idea in practice - the party base may rebel and either sit out general election, or even worse, protest-vote (including writing in Trump, or even Trump running as 3rd Party). Moreover, this dis-satisfaction with the party if that happens may probably sink it 100% longer-term, as it will have no coherent base left at all (with Obama/Trump voters leaving back to DNC, always-Trump voters leaving in protest, and Romney/Clinton voters already have left; and people like me who only vote R as a vote against Democrats will see no point in voting R anymore and probably vote Libertarian as they would have in IRV or other non-FPTP election).
Of course, this handwavey what-if analysis doesn't account for something that would peel off Trump's base support between now and then.
There is no rule saying that the party must nominate Donald Trump. In the past, there have been significant challenges to the incumbent. Pat Buchanan in 1992 and Ronald Reagan in 1976 challenged George H. W. Bush and Gerald Ford respectively on the Republican side. On the Democratic side, Ted Kennedy in 1980 challenged Jimmy Carter. In all three cases, the incumbent lost afterward. Another famous example would be Teddy Roosevelt challenging William Howard Taft in 1912. Again, the incumbent lost to the other party, although it is unclear what would have happened if Roosevelt had not been shot.
In 1928, there was no incumbent running. Calvin Coolidge, the retiring incumbent, disapproved of the leading candidate. He called the other man Wonder Boy and thought that every idea that candidate had proposed while in his cabinet was just plain stupid. However, he also thought that not endorsing him would split the party and cause it to lose in 1928. That candidate was of course Herbert Hoover. Hoover won in 1928, but the start of the Great Depression led to overwhelming Republican losses in 1930-1936. The Republicans would not recover to their 1928 levels until the 2010-2016 period.
Now consider what would have happened if Coolidge had endorsed a candidate that he found more qualified who would have split the party and let the Democrats win the presidency:
- Hoover's Southern strategy would not have become party policy. Without that the Democrats may have continued as the party of slavery with only a few votes from black Americans.
- Either the Great Depression would not have happened, or more likely, it would have happened to a Democrat. Instead of cementing a Democratic majority in the House of Representatives from 1930 to 1994 (with brief interruptions in the 1950s), the Democrats would have been demoralized and discredited.
- The Republicans would almost certainly have won the presidency in 1932 if the Great Depression had still happened. Or in 1936 if it didn't. As it was, Republicans would not win for twenty years.
Compare that to what happened after 1912. Roosevelt disrupted the election to the point that Taft did not win. Republicans were out of power for eight years but came fully back after 1920. Or what happened after 1976. Republicans lost and were out of power for four years but came fully back in 1980. Or what happened after 1992. Republicans lost the presidency for eight years, but won the House for twelve years (1995-2006). Republicans have controlled the House for twenty of the last twenty-four years.
There is considerable precedent for a primary challenge against an incumbent leading to a long term advantage. The only real counter-example is 1980. On the other side, there is that one shining example of not challenging the leader that went horribly wrong in 1928.
It is true that as a practical matter, challenging Trump in the primaries would probably cause the Democrats to win (although that's not certain either). But that might still be better for the Republican party as an organization. Whereas no primary challenge to Trump could easily lead to a really bad result, where disaffected Republicans join the Democrat party in a realignment. Disaffected Republicans could change their registrations so as to vote in the Democratic presidential primaries in 2020. This would only increase Trump's control of what remains of the party, as his candidates would have no effective opposition in the Republican primaries.
If Trump were to win as a Republican in 2020, the result for the rest of the Republican party would likely be disastrous in 2022. This is especially true if the economy runs out of gas after 2020. And in 2024, Republicans would have very little chance. If Trump loses, Republicans would likely maintain in the Senate in 2022 and could make big gains in the House. The 2024 presidential candidate might not win, but 2028 would be wide open.
Is there historical precedent for a party abandoning their previously elected President at the next election?
- 1868 — President Andrew Johnson (D) lost his party nomination to Horatio Seymour.
- 1884 — President Chester A. Arthur (R), suffering from ill health, lost to James G. Blaine.
- 1952 — After losing the New Hampshire primary to Senator Estes Kefauver, President Harry S. Truman (D) withdrew from the race. Illinois Governor Adlai Stevenson would ultimately become the nominee.
- 1968 — In the face of strong primary opposition (from Eugene McCarthy and Robert Kennedy), increasing unpopularity of the Vietnam War, and declining health, President Lyndon B. Johnson (D) withdrew from the race. Ultimately, incumbent Vice President Hubert Humphrey was selected as the nominee.
In all of these cases, the party that failed to renominate the incumbent president would go on to lose the election.