Howard said Sunday that Kearney was given until Monday at noon to resign or she would be fired.
He said the relationship wasn't specifically against school policy, but the rules require someone in a supervisory role to report such a relationship.
"It's not a terminable offense," he said. "She was a perfect coach before and prior to the relationship. She had a pristine record. Why anyone would think she is not a suitable coach is mind-boggling to me."
Ohlendorf called such a relationship "unprofessional and unacceptable."
"We told Coach Kearney and Mr. Howard that such a relationship crosses the line of trust placed in the head coach for all aspects of the athletic program and the best interests of the student-athletes in the program," she said in an e-mail to CNN Sunday night.
Ohlendorf said the school is not naming the student, citing privacy laws.
"We respect her privacy and appreciate her cooperation during our review," Ohlendorf said.
The ex-student reported the former relationship to the school in late October, she said, leading to Kearney being placed on leave in November.
The school said the athlete was an adult when the relationship took place and it had no information that Kearney had any other similar relationships.
The Longhorns' indoor track season begins on Saturday.