A surging presidential candidate is going to war with CNN over its debate rules

Former Hewlett-Packard CEO Carly Fiorina was perhaps the biggest winner of the first GOP debate circuit and she has been climbing in Republican primary polls ever since.

But despite those rising poll numbers, the only woman running on the Republican side may be left off of the stage again next month.

CNN, which is hosting the next debate, weighs heavily polls released before the first Republican debate, when Fiorina was polling around 1%.

The network released rules several months ago announcing that it would average the results of qualifying polls conducted between July 16 and September 10. That average is set to determine the 10 candidates who get to be on the main stage.

The problem for Fiorina is that nine of these polls were conducted before the first debate, according to her campaign, and only two since then.

Fiorina was also excluded during the first main, prime-time debate on August 6. However, she was widely heralded for her strong performance in the "happy hour" debate that hosted the second-tier candidates.

Her poll numbers since then have jumped.

In a new Quinnipiac University poll on Thursday, Fiorina grabbed 5% of the vote, putting her eighth. She also significantly increased her support in several early-primary states: A Public Policy Polling Poll found her in third among New Hampshire Republican primary voters and a Monmouth University poll out this week reported her in fourth in South Carolina.

Fiorina isn't content to simply let the snub slide, however, and her campaign is starting to jab hard at CNN and the Republican National Committee.

"Using all these polls from before August 6 is a little bit like keeping a football team out of the playoffs because of a preseason game," Fiorina said in a Fox News interview Thursday night. "I guess I don't understand why media companies are deciding who Republican primary voters hear from, honestly."

Earlier in the week, Fiorina's campaign slammed CNN and the RNC, accusing both of them of "putting their thumb on the scale."

"If the RNC won't tell CNN to treat post-debate polling consistently with pre-debate polling, they are putting their thumb on the scale," Fiorina spokeswoman Sarah Isgur Flores said in a press release.

Flores ratcheted up the attack even further during a Thursday interview on Fox Business.

"This is the status quo trying to protect the status quo, trying to protect their power, their prestige, and so they want the same people on the stage as before, and they've set up a system that will do that," Flores said.

The Fiorina campaign also took issue with CNN using national polls instead of surveys of the early primary states to determine which candidates to include.

"It's frustrating, to say the least," Fiorina said in yet another Fox interview on Friday. "I'm also comfortably in the top five in virtually every statewide poll that has been taken since that [first] debate - and there have been many. And of course we have statewide primaries, not national primaries."

CNN and the RNC have both defended their methodology, saying that the candidates knew the terms of the debate months ago.

"All the candidates are well aware that, by law, the media set the criteria," the RNC's communications director, Sean Spicer, told Politico. "Candidates - including the Fiorina campaign - had asked that the criteria be well-known before the process. CNN had made the criteria known four months ago."

Fiorina has still benefited from the debates thus far, even if she was excluded from the main show. She's drawing larger crowds at events, and her super-PAC confirmed that the lower-tier "happy hour" debate helped boost fundraising for the super PAC supporting her candidacy.

"We're seeing that with increased fundraising, web traffic, and across-the-board excitement," Carly for America Communications Director Katie Hughes said in an email.

A source close to the campaign framed the fundraising in much more blunt terms.

"I think they're drinking from a fire hose right now," a source told Business Insider.

Many critics had complaints about how the first debate, hosted by Fox News, selected its participants as well.

Polling experts pointed out that the Fox model - which weighted several early polls - was too heavily indebted to name recognition and media coverage that benefited higher-profile candidates. Some experts suggested that the only way to curb the influence of polling bias is to ditch the strict criteria and hold two debates with a random shuffle of candidates in each.

Additional reporting by Colin Campbell.