MOREHEAD, Ky. — A clerk in a rural Kentucky county continued to refuse marriage licenses to same-sex couples Thursday in defiance of a mounting pile of federal court orders that reject her claim that her Christian faith should exempt her from licensing a gay union.

The United States Supreme Court, which two months ago legalized gay marriage across the nation, will now be asked to consider whether Rowan County Clerk Kim Davis can continue to deny marriage licenses until her appeal is complete, a process that could drag out for several more months.

“It’s getting tedious. We get torn down, built back up, torn down, built back up,” said David Ermold. He and his partner, David Moore, have been rejected by Davis’ office twice. “It’s emotionally draining that this keeps happening over and over.”

Days after the Supreme Court’s same-sex marriage ruling, Davis announced that her religious convictions prevented her from sanctioning a gay marriage. She refused to issue licenses to any couple, gay or straight.