Has there ever been an instance when a US president didn't get a second term because they failed to get his party's nomination? From the looks of it, there's nothing that could prevent a sitting US president from getting re-elected other than losing or voluntarily not participating in a general election (typically, due to an unsatisfactory economy). Still, the party that holds the White House, as I understand it, always carries out primary elections across the country.

Do I understand correctly that a sitting president has never been denied renomination and that the process is merely, in practice, a formality?