No first-term President has ever been denied renomination in the modern primary era, but it used to happen fairly often in the old system of the nineteenth century.
There were five first-term presidents in the nineteenth century who failed to get their party’s nomination for a second term.
But importantly, four of them (Tyler, Fillmore, Johnson, Arthur) were “accidental” incumbents who became president only due to another’s death.
The fifth — Franklin Pierce — was the only one who had been elected president in his own right and then was denied renomination four years later. (His replacement, James Buchanan, was *not* an improvement.)
No president in the modern era has been denied renomination, but importantly, every single one who faced a serious primary challenger wound up losing his re-election campaign in the general election.
Ford fended off Reagan in 1976 but then lost to Carter.
Carter held off Teddy Kennedy in 1980 but lost to Reagan.
George HW Bush beat Pat Buchanan in 1992 but lost to Clinton.
The primary challenge didn’t deny them renomination but it hurt them enough to deny re-election.
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