Are primary challenges a bad sign for an incumbent president?

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To use older elections, consider the situation where the incumbent party has a fight for the presidential nomination. One definition of a fight is where one or more rival candidates have a significant number of delegate votes (for instance more than a third) in the first round at the convention.

Since the current two parties in 1860, there have been 37 elections. Only three times did the presence or lack of a fight for the incumbent's party nomination not forecast the winner of the popular vote. Those elections were losses by Nixon (1960) and Hoover (1932), and a win by Garfield (1880).

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Nxion was challenged in 1972

By whom? How successful was that challenge?

John Ashbrook (R-OH). He campaigned actively in New Hampshire, Florida and California, but received less than 10% of the vote.

Also by Representative Paul McCloskey, a "Peace republican."

Nixon received all but one vote at the nominating convention. That qualifies as no challenge.

The nominating convention test is also used in A. Lichtman's 13 Keys to the Presidency. He notes that it is the most powerful predictor in his model.