Updated from April 12 with additional information.

Bill O'Reilly's troubles could be forcing 21st Century Fox's (FOXA)  Fox News to get rid of the embattled star, despite his status as the network's top money-maker. That's according to a story this week in New York Magazine, citing sources close to the matter; at least one institutional investor in Fox has also called for the media giant to deal with the situation decisively. 

The face of Fox's most popular show told viewers during Tuesday night's episode of "The O'Reilly Factor" that he would be going on a pre-planned vacation, prompting many to question what that might mean for his future on the conservative-leaning news network. A Fox News spokesperson told New York Magazine that O'Reilly would return on April 24. O'Reilly said on the air Tuesday that he'd been planning the trip since last fall. 

Shares of Fox were up 1.2% to $31.01 on Thursday. The stock has fallen 0.4% over the last five days, compared to a dip of 0.3% in the S&P 500. 

Gabelli analyst Brett Harris told Bloomberg this week that Fox is "much bigger" than O'Reilly and therefore could probably handle the loss of their top anchor.

"All I can say is we want it dealt with," Harris said. According to the Bloomberg report, Gabelli owns millions of Fox shares; Gabelli is not one of the top 15 institutional holders of Fox's stock, according to Factset, however.

O'Reilly has been the subject of a growing controversy since the New York Times published a report on April 1 revealing that he and Fox News had paid out $13 million to five women who filed complaints of sexual harassment and other behavior. O'Reilly said in a statement that as a public person, he's vulnerable to lawsuits and he's "put to rest any controversies" for the sake of his children.

Fox has since enlisted the law firm Paul, Weiss, Rifkind, Wharton & Garrison to investigate the sexual harassment claims. Paul, Weiss is the same firm that conducted an internal investigation last year into Roger Ailes, the longtime head of Fox News. More than two dozen women, including former Fox News anchor Megyn Kelly, recounted specific claims of sexual harassment to investigators, which ultimately helped seal Fox's decision to dismiss Ailes last July.

In the wake of the report, more than 70 companies have dropped their ads from the "O'Reilly Factor" and shifted them to other Fox programming. Major U.S. advertisers such as Mercedes Benz, Bayer (BAYRY) and ConAgra Foods (CAG - Get Report) have since been replaced with B-list brands including Life Credit Company, "As Seen on TV" belt-maker Comfort Click and Teloyears, a company that claims to have manufactured a genetic test to measure how well a person is aging, according to the Times. In general, marketers have been purchasing significantly less ad time than before the controversy erupted -- there were less than seven minutes worth of purchased ads during last Friday's show, compared to an average of 15 minutes one month ago. 

Despite O'Reilly receiving support from President Donald Trump, calls for his firing have become increasingly louder. At least 1,500 tweets have been posted using the #droporeilly hash tag, according to tracking site hashtracking, and the National Organization for Women last week pressed for Fox to dismiss O'Reilly. Analysts and investors, too, have been calling for Fox to resolve the situation, especially in light of the media giant's pending $14.6 billion purchase of Sky plc (SKYAY) .

21st Century Fox and Fox News are currently grappling with an historic generational shift, in which Rupert Murdoch, 86, has handed over most of the day-to-day operational duties of the company to his two sons, James, the CEO, and his brother Lachlan, who serves as co-executive chairman.

According to New York Magazine, Lachlan and Rupert are said to be in favor of O'Reilly keeping his job, while the younger James Murdoch wants him to be taken permanently off the air, according to New York Magazine. James Murdoch was largely viewed as a key force behind Ailes' departure, noting in the months after his exit that the cable news network's viewership was "stronger than ever." 

Editors' pick: Originally published April 13.

New York Magazine noted that Fox News co-president Bill Shine has advocated for O'Reilly remaining at the network, but that's unlikely to hold much sway in the matter. 

Ever since Rupert Murdoch has become less involved in the day-to-day decisions, the focus at Fox has shifted, said eMarketer analyst Paul Verna. 

"There's been a shift in on-air personalities," Verna noted. "Even if O'Reilly stays, it's very likely there will be a new crop of talent that's coming up and built to last. That will eventually replace the old guard."

Fox has navigated the departure of a primetime anchor before. After Megyn Kelly departed from Fox in January, Tucker Carlson took over the 9 p.m. slot once occupied by Kelly's "The Kelly File." Since then, "Tucker Carlson Tonight" has nearly doubled the ratings achieved by his predecessor, according to The Hill. Additionally, "Tucker Carlson Tonight" saw a 12% spike in viewership in the key 25-to-54-year-old demographic.

It's unclear whether Fox would have as easy a transition if it were to oust O'Reilly, given the nearly four million viewers who tune into the "O'Reilly Factor" each night and the depth of their loyalty. But as Verna points out, those millions of viewers also don't have many other alternatives to choose from in the crop of mainstream cable news networks.

CEO James Murdoch seems less inclined to ruthlessly defend top anchors, instead favoring the "businessman" approach of closely studying the health of the company's bottom line, Verna noted. 

"I think that loyalty has its limits when [it] starts impacting the bottom line," he explained. "When you look at some of the PR struggles that other big companies are having, such as Pepsi (PEP - Get Report) and United Airlines  (UAL - Get Report) , you don't want to be on the wrong side of those."

"There is the adage that all publicity is good publicity, but that certainly has its limits," Verna added.