For only the third time in the 20th century, after the elections of 1912 and 1976, a sitting Republican President was seriously challenged for party's nomination. President George H. W. Bush was challenged by conservative commentator Pat Buchanan, and during the early counting of the votes at the New Hampshire primary, it appeared that the President might actually lose.

However, Buchanan faded by the end of the evening, and Bush won all the rest of the primaries. However, the margins in many of the primaries weren't as large as expected, and led to the rise of Ross Perot as an independent candidate.
George H. W. Bush, President of the United States, 1989 official portrait

George H.W. won the nomination over Pat Buchannan

Pat Buchanan

Pat lost the nomination to Bush.