She was 18, majoring in pre-medicine and settling in for her first year at Kansas State University, her dream school. Barely six weeks later, Crystal Stroup’s college career was suddenly and violently derailed.

In October 2015, after a small get-together at their apartment, her friends got worried because Ms. Stroup had had too much to drink. They enlisted the clean-cut male student from downstairs to look after her while they went out for food.

The next morning, Ms. Stroup woke up disoriented and in pain. Large bruises in the shape of hand prints were emerging on her upper arm and thigh. She struggled to go to class, where she told a friend, “I’ve been raped.”

Kansas State University had been warned about the man, Jared Gihring. Another student, Sara Weckhorst, said she had complained to university officials more than a year earlier that he had raped her while she was passed out drunk at a fraternity house.

On Jan. 3, Mr. Gihring, 22, pleaded not guilty to charges of raping both women. A lawyer for Mr. Gihring, Brenda Jordan, did not respond to requests for comment.

But it was only after Mr. Gihring’s arrest by the police here in July — more than two years after Ms. Weckhorst first complained — that Kansas State took action to expel him.

Whether or not Ms. Stroup’s alleged rape was foreseeable — one of the issues posed by a lawsuit she filed against the university — her case raises disturbing questions about repeat offenses on campus, and whether universities do enough to prevent them.

For several years, researchers have been fiercely debating how many campus rapes are committed by serial offenders. A 2002 study based on surveys of 1,882 college men and published in Violence and Victims, an academic journal, found that as many as 63 percent of those who admitted to behaviors that fit the definition of rape or attempted rape said they had engaged in those behaviors more than once.

But in 2015, a study of 1,642 men at two different colleges was published in JAMA Pediatrics and found that while a larger number of men admitted to behaviors that constituted rape, a smaller percentage of them, closer to 25 percent, were repeat offenders.

The difference could affect how universities approach rape investigations and prevention. For example, repeat cases raise questions of whether universities should be faster to remove students from campus after accusations.

“There are repeat offenders who seek out victims and will do this time and time again with impunity because there is no punishment,” said Annie E. Clark, a co-founder of End Rape on Campus, a nonprofit organization that works to assist those who have been raped and to prevent campus sexual violence. She added, “Whatever the number is, it’s way, way too high.”

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