Most striking, the Browns’ company also has unusually close ties with a pro-Trump PAC, America Fighting Back. The PAC was co-founded last September by Mr. Cain, shortly before The Western Journal absorbed his personal website and began hosting his internet radio show. The PAC’s chief strategist, Todd Ceferrati, is also a consultant to Liftable. Floyd Brown is the PAC’s chairman.

Almost every post on the PAC’s Facebook page is a link to a Western Journal story or commentary. Most of the PAC’s email solicitations are sent out over Liftable-owned domains, according to a Times review, and feature Western Journal stories. A welcome message on the America Fighting Back site celebrates the PAC’s “amazing group of marketing and social media and grass-roots experts dedicated to our nation, President Trump and his agenda.”

Liftable appears to have shut down its backlinking network sometime this year; most of the sites now merely direct readers to WesternJournal.com. Executives said this summer that they had made further changes to the site to hew more closely to Google’s public policies, and appealed the suspension.

But the PAC appears to be a sticking point: In July, shortly after the White House summit, a Google representative told Mr. Brown’s team that The Western Journal was not adequately disclosing to readers its relationship with the political organization. It was hard to tell, the representative seemed to suggest, where The Western Journal ended and the PAC began.

Liftable editors said it had no formal connection to the PAC; the group simply employed Liftable and Firefly as vendors. In an email to The Times, Mr. Brown accused Google of a double standard.

“I challenge Google to remove The Washington Post from Google News because of the political contributions and political activities of Jeff Bezos,” Mr. Brown said. “Americans of all political persuasions used to be allowed their personal political beliefs, but Google punishes our entire company because of my personal giving and activities. All we have ever asked for is to be treated with equality.”

A Direct Line

In mid-August, Patrick Brown told Liftable’s staff he was stepping down as chief executive to take a medical leave. The elder Mr. Brown now runs the family business once again, right as Liftable is fighting for its life. The company has parted ways with some freelancers and left some openings unfilled. Today, according to Floyd Brown, Liftable Media is half its former size.