((Photo: Reuters/Chris Tilley))Lana Bailey holds a placard on the steps of the federal building in protest of Rowan County clerk Kim Davis' arrival to attend a contempt of court hearing for her refusal to issue marriage certificates to same-sex couples, at the United States District Court in Ashland.

The embattled Kentucky clerk at the center of a dispute over same-sex marriage has lost another bid to be exempt from issuing marriage licenses to gay couples based on her Christian faith.

Rowan County Clerk Kim Davis has had her latest appeal to have her office exempt from issuing same-sex marriage licenses rejected by a district judge.

After spending six days in jail earlier this month, Davis was ordered to not stand in the way of her office issuing marriage licenses to gay couples. Davis allowed her deputies to issue the licenses, but did not sign the forms with her authoritative signature, prompting two same-sex couples and two heterosexual couples to sue Davis, arguing that she had altered the licenses in such a way that affected their validity.

Although Davis has repeatedly lost her bid to be exempt from having to follow the Supreme Court order to issue same-sex marriage licenses, she told Fox News' Megyn Kelly this week that she will not resign form her government postion.

"I resign, I lose my voice," she told Kelly. "Why should I have to quit a job I love and am good at?"

Davis added on the Fox News program that this is not the first time she has requested to be exempt from issuing gay marriage licenses. The county clerk also allegedly requested an exemption prior to the June Supreme Court ruling that made gay marriage a constitutional right.

"They can accommodate for all sorts of issues, and we ask for some simple accommodation and we can't receive it," Davis said.