A Dallas appeals court ruled against GOP state Sen. Kim Brimer on Monday in his attempt to disqualify his Democratic opponent, Wendy Davis.

Justice Mark Whittington wrote that the incumbent’s challenge was moot because the deadline has passed to remove a candidate from the ballot. He said the appeal must be dismissed if it “cannot be tried and a final decree entered in time for compliance with pre-election statutes...”

Oral arguments were held last week in front of a three-judge panel of the 5th U.S. Circuit Court of Appeals in Dallas. The case was transferred from the Fort Worth appeals court, but no reason was given.

Bernie Scheffler, spokesman for Ms. Davis’s campaign, said he had expected a quick ruling after hearing justices ask questions about whether it was too late to rule on her eligibility.

“We thought the justices asked all the right questions in their hearing, and we definitely felt good coming out of that hearing,” Mr. Scheffler said.

Jarod Cox, a spokesman for the Brimer campaign, said he had no immediate comment. He said the campaign staff had just received the ruling and was still reviewing it.

Mr. Brimer sued in July to get Ms. Davis removed from the ballot. The lawsuit claimed that Ms. Davis had not officially been replaced on the Fort Worth City Council when she filed to run for Mr. Brimer’s seat.

The Brimer campaign said that would have disqualified her from running for the state Legislature.

A state district judge in Fort Worth ruled in favor of Ms. Davis this summer. Mr. Brimer appealed, but the Aug. 22 deadline for changing the ballot has since passed.

A previous challenge of Ms. Davis’s eligibility also failed early this year. Three members of a firefighters’ association sued to keep her off the ballot, but courts ruled that they had no standing to file the lawsuit.