They say there were a variety of factors at play, including the magazine’s commitment to cultural coverage and its refusal to engage in traffic-driving clickbait. But it also had to do with its often critical coverage of Mr. Trump and other Republicans, as well as the “Never Trump” stance of the magazine’s co-founder William Kristol as he made the rounds on cable television — at times raising hackles at the home office.

Pro-Trump coverage is to conservative media what anti-Trump coverage is to liberal media — a great driver of internet traffic and ratings. The Standard team told potential investors that while it suffered some print subscription losses — down 7,000, or nearly 10 percent, since Mr. Trump’s election, Politico reported — its online subscriptions were up and it had more than doubled its online traffic.

Clarity would not comment beyond its initial statement.

Mr. Kristol started the magazine in 1995 with Fred Barnes and John Podhoretz, with financing from Rupert Murdoch, who sold to Mr. Anschutz, the owner of Clarity Media, in 2009.

The Weekly Standard came to define the “neocon” stance of the Bush era. Its role in making the case for the Iraq war placed it in a camp that had little in common with the views of the more isolationist Mr. Trump, who positioned himself during the 2016 campaign as an anti-interventionist opposed to the Iraq war.

Despite its independent stance, the magazine has been supportive of Mr. Trump’s Supreme Court picks and tax proposals. But its most popular story this week was one by Mr. Hayes, “How Trump’s Lies About Russia Were Exposed.”

And on election night, Representative Steve King of Iowa barred a Standard reporter from his victory reception because of its report that he had referred to immigrants as “dirt” during his campaign.

On Wednesday, I caught up with Mr. Kristol, who is now an editor at large, handing the day-to-day operation over to Mr. Hayes a couple of years ago.