Donald J. Trump’s daunting level of Republican support helped him vanquish a field of presidential primary rivals in under two months.

But he still hasn’t won over one small but crucial group of voters — the men and women who cost him a second term in 2020.

His overwhelming primary victories, including more than a dozen on Tuesday that pushed Nikki Haley from the race, have masked his long-term problems with voters who live in the suburbs, those who view themselves as moderates or independents, and Republicans who backed Joseph R. Biden Jr. in 2020.

On Tuesday, Mr. Trump lost suburban precincts in Virginia despite carrying the state by a staggering 28 percentage points. In North Carolina, his 51-point victory was tempered by much narrower margins in the highly educated and affluent suburbs around Charlotte and Raleigh.

While many Republican strategists anticipate that most Haley voters will eventually support the party’s nominee, Mr. Trump’s failure to bring these voters into the fold less than four years after they helped block him from a second term in the White House raises pressing questions about what he can do in the next eight months to win them over.

He has not seemed especially concerned about this challenge, recently threatening to excommunicate his rival’s donors from his political movement. On Wednesday, he posted on social media that Ms. Haley “got TROUNCED last night, in record setting fashion,” even as he invited “all of the Haley supporters to join the greatest movement in the history of our Nation.”