As he opened his speech at a recent campaign rally in Greenville, N.C., President Trump told the story of the Willie Horton crime case that helped sink the presidential campaign of the Democrat Michael S. Dukakis in 1988.

And then, 30 minutes later, still speaking at the same rally to the same audience from the same lectern, Mr. Trump told the same Willie Horton story all over again, using some of the same language (and getting the facts wrong both times).

Mr. Trump, who last year became the oldest person ever inaugurated as president and turned 80 in June, has demonstrated physical stamina as he barnstorms the country in advance of midterm elections. But his performances on the road and at the White House this fall have produced many head-scratching moments that have revived questions about his age and stability.

He can be forgetful and repetitive. He is more long-winded, more profane and more absolutist than when he ran for president a decade ago. His rambling speeches seem even more garbled at times. He makes comments that leave people wondering what he is talking about or that sound like he is saying something he is not. And even for a president who has never fully observed the norms of the office, he seems more willing to say things no other president would say.