Students walk into the newly renovated Woodrow Wilson Library in Fairfax County. (Erin Schaff/For The Washington Post)

With stellar health benefits and an annual salary of as much as $183,665, the job overseeing Virginia’s largest library system would seem easy to fill.

But several candidates being considered by Fairfax County have decided that they don’t want the job — a reflection, officials and advocates say, of the challenge of finding a top-notch leader when budgets are tight, experts are in high demand and the public is divided over the extent to which libraries should embrace a more digital approach.

Initially hoping to fill the position by the end of this year, Fairfax officials have temporarily called off the nationwide search to replace Samuel Clay, the library director who is set to retire in March and has been pilloried by booklovers angry about Clay’s efforts to make county libraries less about print.

A person who was offered the director’s job this month declined to take it, saying the area’s cost of living is too high, Fairfax officials said. Two other applicants withdrew from consideration after being interviewed, saying they didn’t think they were “a good fit” for the county, said Karrie Delaney, vice-chair of the county’s Library Board of Trustees.

Citing confidentiality rules, county officials declined to identify the applicants.

“We were thrilled” about getting close to hiring someone, said Charles Fegan, chair of the library board. “And, then, out of the blue, I got a telephone call or e-mail from the Human Resources Department saying that the person had rejected the offer and would not consider it under any circumstances.”

Fegan notified the rest of the board last week that the search had been suspended. The hunt for qualified candidates will pick up in January, he said: “It’s better to let the water settle for a minute before we jump into it again.”

Many public library systems — including Fairfax’s — are facing budget cuts that in some cases have forced officials to close branches or reduce their hours of operation.

Meanwhile, more library directors appear to be retiring. And their potential replacements, who have expertise in information science that has become a prerequisite for the job, are also in demand for higher-paying positions in the private sector requiring those same skills, library officials say.

Since 2011, 22 directors of Virginia public library systems have retired, and by April, three more — including Clay — are expected to step down. There are about 90 library systems in the state.

“There are more openings and fewer people with the skill sets to take on library directorships,” said Sandra G. Treadway, the state librarian. “It’s a competitive marketplace.”

In Fairfax, the next library director will take over a system whose annual budget — $27.6 million — is 17.5 percent lower than it was in 2008. Fewer people are visiting county libraries: There were about 4.1 million last year, down 625,000 since 2011. During that same period, e-book circulation has grown from 220,000 to 1 million.

With the budget cuts have come a reduction in hours of operation, unfilled staff positions and a diminishing stockpile of books, as county librarians turn more to digital offerings and weed outdated collections from the shelves.

Since 2004, the number of volumes in Fairfax libraries has shrunk by about 440,000, to about 2.3 million, triggering the ire of library advocates who worry that a central part of life in the affluent suburb is disappearing.

Those advocates were outraged two years ago to discover that some branch libraries were throwing away old books rather than donating them or offering them for sale. A long-term plan for the system that would have reduced the number of employees and lowered the qualifications required for branch librarians also elicited strong criticism.

“The county is in desperate need of having a first-rate library director who can turn around a floundering system,” said Dennis K. Hays, head of Fairfax Library Advocates, a group of county residents pushing for more library funding.

He speculated that candidates are turning away from the top job because they have “not gotten the assurance that they will have the support that is required here.”

Sharon Bulova, chairman of the County Board of Supervisors, said that libraries remain a high priority in Fairfax. But she wouldn’t rule out additional funding cuts as the county struggles with expected deficits.

“We will be talking about programs in libraries,” said Bulova (D). “But I do not see our doing anything that could jeopardize the quality that people can expect in our libraries.”

Next month, the county will survey residents on what they want from their libraries. The task ahead for any new director will be to innovate, said Delaney. Already under consideration: creating entre­pre­neur­ship centers in libraries for people seeking to learn how to launch a business.

“If we can consider not just priorities of how to allocate money but creative ways to make the library something that everyone can see value in, I think that’s where we’ll be able to position ourselves to secure the funding we deserve,” Delaney said.