Updated 5:40 p.m. ET

The felony invasion of privacy case against Missouri Gov. Eric Greitens can continue, Circuit Judge Rex Burlison ruled in St. Louis on Thursday. Many of Greitens' fellow Republicans have urged him to resign; he has refused.

Burlison announced he would not dismiss the case in response to a motion from Greitens' defense team, reports St. Louis Public Radio's Jason Rosenbaum.

Greitens is charged with a felony for allegedly taking a photo of a naked woman without her consent. His lawyers said the case should be thrown out because of the conduct of the St. Louis circuit attorney's office.

The defense had accused prosecutors of withholding evidence, and said a private investigator hired by the prosecution had lied to the court. The judge agreed that the prosecution acted badly, but imposed lesser sanctions rather than throwing out the entire case.

The trial is scheduled for May 14.

The invasion-of-privacy case is one part of a larger scandal that has embroiled Missouri politics since January, when Greitens acknowledged an extramarital affair. The allegations that arose since then have led to the possibility that Missouri's governor could face an impeachment effort from the legislature his own party controls.

As Jason Rosenbaum reported on Morning Edition on Thursday:

"The developments quickly gained steam: In February, he was indicted for photographing the woman he had an extramarital affair with without her consent. And last week, a detailed investigation by the Missouri House painted the former Navy SEAL as being sexually and physically abusive in the affair.""While the governor admitted to the affair, he's strenuously denied the woman's characterizations of his behavior. And he's made it clear for months that he's not going to resign."

The woman with whom he had the affair has described Greitens taking a photo of her while she was bound, nude and blindfolded, and then threatening to blackmail her with the photo if she told anyone about their relationship.

The felony charge of invasion of privacy centers on the existence of the photo, not any blackmail threat. Prosecutors say by taking such a photo and saving it to a computer, Greitens violated state law.

Prosecutors do not have the photo in their possession.

Greitens' defense team asked a judge to throw out the case, accusing St. Louis Circuit Attorney Kim Gardner of misconduct, as St. Louis Public Radio reports:

"In multiple motions filed over the last several days, Greitens' legal team accused Gardner of failing to turn over evidence in a timely fashion — first, a videotape and notes from an interview done with the woman at the center of the case, and then notes from an interview with a confidant of the woman's. Each time, defense attorneys said, the missing evidence was helpful to their case because it called the woman's credibility into question."

Defense lawyers also accused a former FBI officer Gardner hired as a private investigator of lying to the court under oath.

The judge agreed that the prosecution's conduct "is not to be condoned and it is serious." But instead of throwing out the case, he is allowing Greiten's lawyers to take more depositions of key witnesses.

Greitens has called the case against him a "witch hunt." And this week, he filed for a temporary restraining order against Missouri Attorney General Josh Hawley — another fellow Republican. That motion relates to potential new felony charges, which the attorney general says there's enough evidence to bring against the governor over his campaign practices.

On Tuesday, Hawley alleged "that Greitens took a list of donors to his military veterans charity, transferred it to his political campaign, and used it for political fundraising," as we reported.

Hawley has sent that evidence to St. Louis Circuit Attorney Kim Gardner, whose office is reviewing the information.

As Jason Rosenbaum reports from St. Louis, "Hawley is running for the Senate against Democratic incumbent Claire McCaskill. And observers say he may be worried that the governor's woes will hurt his chances."

It's a stark turnabout for Greitens, 44, who won the governor's office in 2016, succeeding Democratic Gov. Jay Nixon after recording an upset win in the Republican primary. The victory had put him on the map as a rising star in his party, in a state that had sided with President Trump in the 2016 vote.

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