Of all the tribulations facing Donald J. Trump, perhaps none is stirring as much anxiety inside his campaign as the precipitous decline of support from Republican women, an electoral cornerstone for the party’s past nominees that is starting to crumble.

In a striking series of defections, high-profile Republican women are abandoning decades of party loyalty and vowing to oppose Mr. Trump, calling him emotionally unfit for the presidency and a menace to national security.

But even more powerfully, his support from regular Republican women is falling after Mr. Trump’s provocative remarks about everything from the silence of the mother of a slain Muslim soldier to how women should respond to sexual harassment in the workplace.

“For people like me, who are Republican but reasonable and still have our brains attached, it’s hard to see Trump as a reasonable, sane Republican,” said Dina Vela, a project manager in San Antonio who said she had always voted Republican and remained wary of Hillary Clinton. But to her own surprise, she has started visiting Mrs. Clinton’s campaign website and plans to vote for her.