Mr. Biden’s campaign advisers and allies insist that Mr. Biden is as physically and mentally sharp as ever. They plan to implicitly knock down any suggestion that his gaffes reveal a candidate past his prime by suggesting that his cringe-inducing comments are nothing new and that voters are already used to his propensity for misspeaking.

“Joe Biden has spoken his mind his entire life, which voters know and love about him,” said Kate Bedingfield, Mr. Biden’s communications director and deputy campaign manager. “He’s a real person, he’s authentic and that will never change.”

The Rev. Joseph Darby of South Carolina, who considers Mr. Biden a longtime friend, was blunter as he emphasized that “Joe’s always been gaffe-prone — it’s just a piece of who he is.”

“He made a bunch of them last week but I don’t think it affects his capacity to govern,” added Mr. Darby, who for professional reasons has not endorsed a candidate but expressed a view shared by many Biden supporters. “He is as sharp as he’s been. You’re running against Donald Trump, for chrissake. Donald Trump has had his own share of gaffes, numerous gaffes, on top of falsehoods, on top of bigoted insults.”

Of course, a political strategy of highlighting that your own candidate has long committed verbal blunders is not the ideal method of damage control. But advisers said privately that there was little they could do to change Mr. Biden’s speaking style, even as they were quick to fault the news media for, in their view, blowing missteps out of proportion.

They argue that rank-and-file voters care less about his misstatements than the news media and the liberal activists on Twitter, pointing to Mr. Biden’s lead in national and most early-state surveys. They also note that he has survived far bigger controversies this summer without losing his front-runner position in the polls.