“Somebody at 80 years old just doesn’t have the physical stamina, the mental stamina for that office,” said Rahm Emanuel, a prominent Democrat who is interested in running for president in 2028, and who has called for a mandatory retirement age of 75 for many top federal positions. Mr. Emanuel, who served as a chief of staff to President Barack Obama and a top aide to President Bill Clinton, said that the presidency is especially taxing.

“It ages you in a way that no other stress in your life does,” he said.

Some White Houses have been more aggressive than others at obscuring the truth of an aging president’s condition. As President Joseph R. Biden Jr. physically declined, his aides went to great lengths to obscure the signs of his aging. No one in Mr. Biden’s inner circle discouraged him from trying to run for the presidency again, despite indications that he was growing more frail.

As he ages, Mr. Trump has taken a different approach. He lets the cameras pick up his slumps, swollen ankles and bandaged hand. He continues to take a tall stairway wheeled up to Air Force One, often navigating the stairs carefully. He continues to appear before the news media, fielding questions from friendlier faces and lashing out at journalists who ask him questions he perceives as unflattering.

More often than not, he meanders far beyond the topic he has appeared before reporters to discuss.

“These are the strongest job numbers of the entire administration so far, and that’s during this conflict, on top of it. So it’s great. And, you know, we have a thing. We have a problem in this country, because it used to be, if you’re — I’m a little older than a couple of you, but I don’t feel old. I feel the same as I did 50 years ago. It’s crazy. Mr. Senator. We got a great Senator right here, Ron, but I do feel the same. But — but in the old days, you know, if you had good job numbers, like great job numbers like they announced today, the stock market goes up. Today, everything is crazy,” Mr. Trump said to a group of supporters in Wisconsin earlier this month, slipping an aside about his age into a monologue on other topics, including the U.S. war in Iran, his thoughts about the stock market, and a greeting for Senator Ron Johnson, Republican of Wisconsin.

The presidential historian Julian E. Zelizer, who has edited a book about the Trump presidency, said that it is hard to know what elements of Mr. Trump’s erratic behavior and meandering speech patterns can be attributed to age-related decline.