Donald Trump talks to reporters in the "Spin Alley" after the first prime-time presidential debate hosted by Fox News and Facebook at the Quicken Loans Arena Thursday, Aug. 6, 2015 in Cleveland. Scott Olson/Getty Images

Since announcing his presidential run, Donald Trump has blown up his relationships with NBCUniversal, Telemundo, Univision, the PGA Golf League and a handful of other institutions. It's been part of his charm. But after the first GOP debate in Cleveland on Thursday, has the eccentric billionaire lost Fox News too?

"I'm very surprised at Fox News," Trump vented on MSNBC's "Morning Joe" on Friday morning, complaining that the conservative channel's relentlessly hyped debate was rigged against him. "I would say it's pretty unprofessional, but we will live with it."

As usual, Trump was looking out for himself -- but does he have a point? After three months of giving Trump more hours of coverage than any other candidate, Fox News appeared to relish popping his balloon on national television.

The tone was set from the very first question, when the stony-faced moderator Brett Baier asked all the candidates whether they would support the eventual Republican nominee without running as an independent and potentially splitting the party. Trump alone refused to make that promise.

"Mr. Trump, to be clear, you're standing on a Republican primary stage," Baier said. "An independent run would almost certainly hand the race over to Democrats and likely another Clinton. You can't say tonight that you can make that pledge?" The boos from the crowd put Trump on defense for the rest of the debate.

Even more brutal was Megyn Kelly's clean shot at Trump's misogynistic remarks about women. Challenging him to explain whether calling women "fat pigs" was presidential, Kelly earned cheers from liberals and Fox fans alike. (For good measure, Trump retweeted a fan of his early Friday who called Kelly a "bimbo.")

Is Fox looking to pump and dump the mogul -- to build him up only to knock him down?

The channel has certainly done its part in helping him rise: In June, Trump racked up one hour and 48 minutes of airtime on Fox, ahead of Rick Perry (an hour and 25 minutes) and Jeb Bush (52 minutes), according to the liberal watchdog Media Matters. In May, he gobbled up two hours and 39 minutes, surpassing Mike Huckabee, Bush and Perry.

Including minutes in July, that's 4 hours and 45 minutes.

But as CNN's Brian Stelter noted on Friday, Fox owner Rupert Murdoch is no fan of the front-runner. He's called Trump "embarrassing," and weeks ago reportedly asked Fox News boss Roger Ailes, his employee, to ease up on Trumpmania, to no avail.

A Fox representative did not immediately respond to request for comment on Trump's accusations.

Trump certainly has a habit of complaining about his treatment from the media, calling out MSNBC just a few weeks ago for not mentioning his name enough. But if Fox News is souring on the ex-reality TV star, that's a serious predicament for anyone looking to make a pitch to conservatives across the country.

The channel does have a reputation for looking out for the interests of the Republican Party above all else, from both its critics and its supporters. As Baier's first question implied, Trump is now seen as a threat to the strength of that party, jeopardizing a nice clean nomination. If he doesn't address that, Trump may be in the doghouse with Murdoch's empire for the rest of his run.