The ruling Saturday was the second in as many days from U.S. District Judge Marvin Shoob, who on Friday issued a preliminary injunction barring NASCAR from stopping AT&T Inc. from placing its brand on Burton's Richard Childress Racing Chevrolet.
Following Saturday's denial for a stay, NASCAR filed an emergency appeal with the 11th U.S. Circuit Court of Appeals in Atlanta.
"We don't know when that will heard," said NASCAR's managing director of corporate communications Ramsey Poston.
"Our expectation going in is that it probably wouldn't be heard until next week."
Shoob's decision to deny NASCAR's request for a stay followed a private hearing.
NASCAR has tried to prevent the Cingular logo from being changed to the AT&T logo on Burton's car. AT&T is the sole owner of Cingular and is rebranding the cell phone company's name to AT&T.
After Friday's ruling, AT&T announced that Burton's car will be repainted in time for Saturday's Nextel All-Star Challenge at Lowe's Motor Speedway in Concord, N.C.
Sprint Nextel Corp. sponsors NASCAR's premier series, the Nextel Cup, and has exclusive rights as the telecommunications company for the series. Attorneys argued the only exceptions are companies, including Cingular, that already sponsored cars when Nextel reached its agreement with NASCAR.
San Antonio-based AT&T became the full owner of Atlanta-based Cingular when it completed its purchase of Atlanta-based BellSouth Corp. in December.
Cingular argued that its rights included changing its brand name to AT&T.
Shoob said forcing Burton's car to continue to carry Cingular's brand would only confuse fans.
"The court concludes that the continued appearance of the Cingular brand on the No. 31 car, unaccompanied by any indication that Cingular now does business as AT&T, is likely to confuse NASCAR fans," Shoob wrote.
Shoob also concluded that AT&T has shown it will suffer irreparable harm in the form of loss of goodwill and loss of exclusive rights to renew its sponsorship agreement unless the court issues the injunction.
NASCAR argued that Nextel was entitled to exclusivity through its 10-year, $700 million investment that began in 2004. It also said it could be sued by Sprint Nextel if the court granted the injunction in favor of AT&T.
"Regardless of whether Sprint Nextel could or may bring suit against NASCAR, the court finds that the threat of such a suit does not outweigh the actual and imminent irreparable harm plaintiff will suffer if the court does not issue an injunction," Shoob said in his ruling.
The No. 31 car has been sponsored by Cingular Wireless LLC since 2001. Cingular had been a joint venture of AT&T and BellSouth before AT&T purchased BellSouth.