The number of federal investigations into how colleges handle sexual violence reports has jumped 50 percent in the past six months, reflecting a surge of recent discrimination claims and the difficulty of resolving high-profile cases that often drag on for years.

On May 1, the Education Department’s Office for Civil Rights released the first public list of colleges and universities under scrutiny for possible violations of federal law in their responses to sexual violence allegations.

At the time, 59 cases were pending at 55 schools. As of this week, 89 cases are pending at 85 schools. Eight cases are more than three years old, including one focused on the University of Virginia, one on Harvard Law School and one on Princeton University.

The rapidly rising total poses challenges for the Obama administration as it seeks to lead a national campaign against sexual assault on college campuses. The students whose complaints sparked many of the cases are anxious for federal action, while colleges want to escape a list that puts an unflattering question mark next to their brand name.

Catherine E. Lhamon, assistant education secretary for civil rights, said more students are turning to her office, known as OCR, for help as they have become aware that the government is willing to intervene to guarantee fair treatment.

“The list is growing partly because we’ve told people we will be there for them,” Lhamon said. “And there’s value in coming to us. I’m really pleased that people trust us — and hope to earn that trust.”

Some higher education officials wonder why the government can’t accelerate. “At some point, that list will be so big it will be meaningless,” said an official at one West Coast school who spoke on the condition of anonymity because the school is under federal investigation.

Lhamon said OCR’s staff has shrunk — to 544 full-time positions this year from 619 in 2011 — as its workload has grown. Its mandate is to prevent discrimination on the basis of race, ethnicity, age, disability or gender in federally funded schools. Sexual violence issues at colleges account for a small share of the agency’s cases.

Lhamon, who took office in August 2013, said she wants, as often as possible, to resolve investigations within six months. “I have made it a priority to close out our old cases as quickly as we can,” she said.

But since May 1, just two schools have dropped off the sexual-violence investigation list.

In June, OCR closed a six-month probe of the State University of New York at Binghamton because it determined that the issues at hand were covered through a previous accord with the SUNY system. In September, OCR resolved a four-year-old case at Ohio State University after investigators found that written policies and procedures for responding to reports of sexual violence and harassment did not follow requirements of the anti-discrimination law known as Title IX.

Schools under OCR scrutiny are generally loath to say anything about the cases beyond affirming cooperation with the government. Officials at U-Va., Harvard and Princeton declined to discuss the longevity of inquiries into their schools. The U-Va. case began in June 2011. The Harvard Law and Princeton inquiries date to December 2010. (A separate investigation of Harvard College, the main undergraduate unit of the university, began six months ago.)

Harvard and Princeton this year announced new policies on sexual violence, which could clear the way for ending their OCR investigations. But 28 current and retired members of the Harvard Law faculty have criticized the university’s action, saying it failed to provide due process protections to accused students.

“Harvard apparently decided simply to defer to the demands of certain federal administrative officials, rather than exercise independent judgment about the kind of sexual harassment policy that would be consistent with law and with the needs of our students and the larger university community,” the professors charged Tuesday in an opinion column published in the Boston Globe.

The university said its policy provides “an expert, neutral, fair, and objective mechanism for investigating sexual misconduct cases involving students.”

Much of OCR’s power stems from its authority to halt federal funding to colleges found to be in violation of the law. But the agency has never taken that step.

Instead, OCR uses the financial threat as leverage to negotiate measures schools will take to improve their sexual violence policies whenever the agency finds shortcomings. Those negotiations are sometimes prolonged.

The schools under investigation represent a broad swath of higher education: a community college district in California, a state university system in Alaska, two professional schools, several liberal arts colleges and dozens of public and private universities.

Catholic University is under scrutiny in the District. Listed from Maryland are Johns Hopkins University, Frostburg State University and Morgan State University. In addition to U-Va., Virginia schools on the list are James Madison University, the College of William and Mary, the University of Richmond and Virginia Military Institute.

Investigations can begin in two ways: through a complaint from an individual or through a government decision to examine records and policies in what is called a “compliance review.”

Interviews with officials at four of the 85 schools on the list — all speaking on the condition of anonymity because their cases are pending — cast light on how investigations proceed. First, a regional unit of OCR notifies a school of a new case. Then, it makes a substantial request for records and information. It might summarize an allegation from an individual, if there is one, and ask for the school’s version of what happened. The request typically seeks records on sexual violence incidents for the previous three years, as well as information on the school’s protocol for response and discipline.

There might be phone calls between the school and OCR to hone or clarify the request. All of this can take several weeks. “It’s a lot of time. A lot, a lot of time,” said the West Coast school official. “We produce so much material. They’re going to look at all your policies, all your practices.”

Eventually, OCR schedules a visit. This can occur several months after the investigation begins. Focus groups are organized to talk with OCR about issues related to sexual harassment and violence. The groups might be drawn from faculty, staff, student-athletes, resident assistants, fraternity members, sorority members and campus organizations.

Schools must give public notice of the OCR visit, disclosing information on how to contact investigators. One official at an East Coast school under investigation said the school was not allowed to observe OCR’s meetings with focus groups or other community members. “We have no idea what they’re going to be told, who is telling it, who may have a biased or skewed version of the facts,” the official said.

Sometimes, OCR makes multiple campus visits. Afterward, schools wait as the inquiry continues. At some point, the regional unit of OCR sends preliminary findings to Washington. Final determinations and settlements come from headquarters. Some school officials complain that they are not likely to be shown any draft findings before they are made public.

In April, Tufts University rebelled. The prestigious university in Massachusetts had reached an agreement for measures to resolve a long-running OCR investigation. Then, it abruptly revoked its approval, objecting to certain findings that the university failed to comply with the law in its handling of sexual assault and harassment complaints.

Federal officials warned the standoff could lead to an unprecedented cutoff of funding for Tufts. A few weeks later, the university relented and gave renewed approval to the resolution. The episode offered a rare public glimpse of the brinkmanship behind these investigations.

An official at another East Coast school under investigation said the school simply wants to cooperate and move forward, as fast as possible. “Right now, we’re just sort of hanging,” he said, “waiting for them to tell us what needs to change, what doesn’t need to change.”