On Monday night, Andrew Rosen, the chief executive officer of Kaplan, sent a memo to employees about the blockbuster news that their parent company, The Washington Post Co., was selling its flagship newspaper.

Rosen’s message: The world will soon realize that Kaplan, which owns a chain of for-profit colleges, is crucial to the rest of the company’s prospects.

“For some years now, Kaplan has been the largest part of the Washington Post Co., and the most important determinant of its economic future,” Rosen wrote. “That wasn’t always fully understood by the broader market. It will be now.”

Kaplan’s role poses challenges for the company as for-profit colleges struggle with declining enrollment amid renewed competition from traditional colleges. For the past three years, President Obama’s administration, Congress and state and federal authorities have scrutinized for-profit colleges’ marketing, job-placement claims and their students’ debt levels.

“Kaplan is a piece of a much larger story about the emergence of the for-profit education model that had its gilded age and is now facing its demise in the face of what we know about the horrible outcomes in the sector,” said Barmak Nassirian, director of federal policy at the American Association of State Colleges and Universities in Washington.

In 2012, The Washington Post Co. — which plans to change its name with the sale of the newspaper to Amazon.com CEO Jeff Bezos — derived more than half its $4 billion in annual revenue from education businesses.

Until several years ago, revenue and earnings growth at its Kaplan for-profit colleges helped offset declines at its newspaper.

Last year, amid declining enrollment, Kaplan said it stopped signing up students at nine campuses and was folding four others into nearby locations. Kaplan reported a $105.4 million operating loss for 2012, mostly because of restructuring costs and noncash charges related to the diminished value of the business.

Total enrollment at Kaplan University and Kaplan Higher Ed campuses plunged almost in half to 62,192 students at the end of the second quarter from 112,221 two years earlier.

Declines in revenue and students continued in the first six months of this year, though the company said it had an uptick in the number of new students signing up for classes.

“The higher education business is clearly the engine that needs to drive this business,” said Peter Appert, an analyst with Piper Jaffray & Co. in San Francisco who follows for-profit colleges. “I’m of the view that the for-profit post-secondary education industry is going to face significant challenges for the foreseeable future.”

The worst may be over for the Kaplan business, said Mark Hughes, director of research at Lafayette Investments in Ashton, Md., which manages $350 million and owns Washington Post shares.

Hughes cited the increase in new students signing up for Kaplan programs in the second quarter. The education division posted about $350 million in operating profit in 2010 and though it might not return to that level, it could well recover some of its past earnings power, he said.

“We’re closer to the point where the for-profits have their wind at their back than we have been during that last three or four years,” Hughes said.

Kaplan’s financial results are showing “steady improvement,” said spokeswoman Melissa Mack.