(Erin Patrick O'Connor/The Washington Post)

Is Bill O’Reilly too big to fire?

The question wouldn’t even have been asked just a few days ago. The most popular attraction on cable, O’Reilly seemed to be Fox News Channel’s indispensable man, the embodiment of its pugnacious identity. With record ratings behind him, he re-upped at Fox only last week, reportedly for a knee-buckling $18 million a year.

Now? The question is plausible, but the likely answer is unsatisfying: It depends — on multiple, unpredictable factors.

The opinionated host of “The O’Reilly Factor” was ushered into his own no-spin zone Saturday with the publication of a damning New York Times article documenting a succession of sexual-harassment complaints against him. The article provided some grim math: O’Reilly and Fox have paid $13 million over the past 15 years to settle five cases (three unreported until the Times article) involving women O’Reilly had worked with.

Fox had nothing to say in O’Reilly’s behalf on Wednesday, but he did get an attaboy from an old friend. President Trump called O’Reilly “a good person” in an Oval Office interview with Times reporters, adding this bit of legal advice: “Personally, I think he shouldn’t have settled. Because you should have taken it all the way. I don’t think Bill did anything wrong.”

Advertisers including GlaxoSmithKline, Allstate and Hyundai have deserted Bill O’Reilly’s Fox News Channel show. (LEFT: AP photos; RIGHT: Reuters)

Nevertheless, according to media reports, more than 30 advertisers have flown away from O’Reilly’s program like a flock of startled sparrows since the harassment article emerged. Major companies such as BMW and Hyundai said they were “suspending” their ads on the show until — well, it’s not clear when “until” is.

And that could be one, if not the, decisive factor in “The O’Reilly Factor’s” continued existence. A sustained and widespread advertiser shunning of O’Reilly would be painful, undermining a key economic rationale for his program. Such was the case for Glenn Beck, who proved to be a popular attraction for Fox News between 2009 and 2011 but whose radioactive commentary made him persona non grata with Fox’s advertisers. Beck and Fox parted ways after 30 months.

But advertiser boycotts are hard to sustain, especially when the audience remains loyal. Rush Limbaugh proved resilient when facing advertiser defections in the wake of his disparaging comments about birth-control advocate Sandra Fluke in 2012. Many of the initially reluctant advertisers eventually came back to Limbaugh.

On the other hand: Don Imus. The radio and TV personality walked into a wall of outrage when he made some racially charged comments in 2007. Advertisers quickly fled, employees of CBS Radio and MSNBC complained, and within days Imus was off the air.

O’Reilly’s fate ultimately lies not with any corporation but with three men named Murdoch. Patriarch Rupert Murdoch, the co-founder and acting chief executive of Fox News, has gradually ceded power within his media empire to his sons, James and Lachlan. Together, the trio sits atop 21st Century Fox, Fox News’s parent.

One consideration in the Murdoch Rubik’s Cube of business interests is 21st Century’s $14 billion bid to buy Sky TV, the British satellite service. The Murdochs abandoned an earlier bid for Sky in 2011 amid another mess in their house, the phone-prying scandal perpetrated by employees of Murdoch’s News of the World tabloid. A parliamentary panel later said Rupert and James Murdoch were “unfit” to run a public company — an adjective that could haunt them again if the O’Reilly matter intersects with British approval of the Sky takeover.

The sons, however, were instrumental last year in standing up to their father over Fox News’s other co-founder, Roger Ailes, eventually ousted amid a cascade of sexual-harassment allegations against him. They vowed at the time to improve the apparently toxic culture that Ailes had fostered, saying, “We continue our commitment to maintaining a work environment based on trust and respect.”

(Erin Patrick O'Connor/The Washington Post)

The O’Reilly revelations, and another harassment lawsuit filed Monday by Fox contributor Julie Roginsky, suggest they may still have some work to do.

“If the Murdoch sons were going to change FNC’s culture, [former host] Megyn Kelly would not have jumped ship,” said Andrew Tyndall, a veteran network news analyst. “I took her departure to indicate that this was still the House That Roger Built, even in his absence.” (Kelly joined NBC News in January.)

If so, he said, “O’Reilly’s transgressions are not firing offenses but par for the course, and whatever financial hit they incur is the cost of doing business.”

In fact, advertising losses, if any, are just one part of the financial picture for Fox. The bulk of revenue for cable networks come from cable and satellite providers that deliver the programs to viewers. And this money flows from long-term contracts, unaffected by momentary controversies.

In this regard, what O’Reilly’s audience does, rather than his advertisers, may be of greater importance to Fox’s bottom line. The massive “Factor” audience, some 4 million viewers per night, helps Fox make its case to cable operators that they should continue to pay ever-rising fees to carry the channel, Tyndall points out.

And O’Reilly’s audience has been hyper-loyal, even during (or perhaps because of) the host’s various controversies. When O’Reilly was under fire in 2015 for serial exaggerations about his exploits as a reporter, his ratings got a modest bump. He weathered that storm by painting himself as the victim of an orchestrated campaign by the liberal media. Variations of this strategy colored a brief dust-up involving Al Sharpton in 2007; a lurid, tabloid-worthy sexual-harassment case in 2004; and his defense against reports of spouse abuse during his divorce in 2015.

In this latest controversy, O’Reilly, while not denying the Times report, portrayed himself as a victim of money-hungry opportunists.

Still, those who oppose O’Reilly dream his latest scandal will be his undoing.

“We know the Murdochs don’t care about racism or sexism. They care about the bottom line,” said Rashad Robinson, executive director of Color of Change, a civil rights organization that has been involved in campaigns against Beck, Imus, Limbaugh and then-CNN anchor Lou Dobbs. “And they will care when Bill O’Reilly isn’t making as much money.”

To that end, Robinson said his group intends to remind advertisers that “they can’t just wait it out three weeks before they start buying ads [on O’Reilly’s program] again.”

But Robinson isn’t making any predictions about how his campaign, and O’Reilly, will end up. “I think it’s too early to tell,” he said.