Advisers who once hoped a Pygmalion-like transformation would refashion a crudely effective political showman into a plausible American president now increasingly concede that Mr. Trump may be beyond coaching. He has ignored their pleas and counsel as his poll numbers have dropped, boasting to friends about the size of his crowds and maintaining that he can read surveys better than the professionals.

In private, Mr. Trump’s mood is often sullen and erratic, his associates say. He veers from barking at members of his staff to grumbling about how he was better off following his own instincts during the primaries and suggesting he should not have heeded their calls for change.

He broods about his souring relationship with the news media, calling Mr. Manafort several times a day to talk about specific stories. Occasionally, Mr. Trump blows off steam in bursts of boyish exuberance: At the end of a fund-raiser on Long Island last week, he playfully buzzed the crowd twice with his helicopter.

But in interviews with more than 20 Republicans who are close to Mr. Trump or in communication with his campaign, many of whom insisted on anonymity to avoid clashing with him, they described their nominee as exhausted, frustrated and still bewildered by fine points of the political process and why his incendiary approach seems to be sputtering.