Correction: The article about veterans’ disability claims incorrectly said that children were airlifted from South Vietnam as part of Operation Babylift after the fall of Saigon in 1975. The airlift occurred before the fall of the capital city. This version has been corrected.

As President Obama’s first term winds down, his administration has reported significant progress in combating several high-profile veterans problems, including reducing unemployment and homelessness.

But in another key area — the backlog of disability claims — the problem has worsened under Obama’s watch, spurred by an influx of new veterans into a weak economy, new rules that make it easier to file claims, including for Agent Orange-related conditions and post-traumatic stress, and a growth in the average number and complexity of medical conditions claimed by veterans.

When Obama took office in January 2009, the number of pending claims at the Department of Veterans Affairs was 391,127. As of Nov. 3, that number was 896,409, including 570,970, or 66 percent, that have been pending longer than 125 days.

VA Secretary Eric K. Shinseki vowed two years ago to “break the back of the backlog by 2015,” promising claims would be processed within 125 days, with 98 percent accuracy. The VA says it is on track to meet its goal.

“I have no doubt we will get there,” Under Secretary for Benefits Allison A. Hickey said Tuesday.

Hickey, a hard-charging retired Air Force general, is overseeing the department’s effort to transform the system from an antiquated, “1950s industrial age” process into one that is faster, more accurate, paperless and digital.

“We’ll have the tools this organization has never had before,” she said, noting the deparment has launched a number of initiatives and experimental approaches to tackle the problems.

Hickey, the daughter of a retired Army lieutenant general, is a 1980 graduate of the U.S. Air Force Academy, the first class to include women. She logged more than 1,500 hours of flight time as a pilot and commander in Air Force tankers and other aircraft, and later served as director of the Air Force’s Future Total Force office at the Pentagon.

Since taking office in June 2011, Hickey has won the trust of veterans’ organizations with her attempts to shake the VA bureaucracy and her willingness to tackle problems with late-night e-mails and phone calls.

“Hickey is by far the most energetic and focused” person to hold the job, according to Gerald Manar, deputy director of national veterans service for the Veterans of Foreign Wars.

But veterans groups remain skeptical about the VA’s 2015 target for erasing the backlog and improving claim accuracy.

“Over the past two years, VA has gone backward, not forward, in both these key areas,” American Legion National Commander James E. Koutz recently testified before Congress. When Shinseki made his pledge, 37.1 percent of claims were pending for more than125 days, compared with the current 66 percent.

In addition, the decisions rendered by examiners are often rife with errors. The American Legion was involved in 6,190 cases brought to the Board of Veteran Appeals in Washington through the first nine months of 2012. More than three-quarters of the board’s rulings found problems with the VA’s decisions, the American Legion said. Among those, 49 percent were remanded to the regional office for review and 28.6 percent were overturned.

A report released Friday by the Center for a New American Security, a Washington-based think tank, called the problem the “primary” area in need of improvement among federal government services for veterans. “The enormous backlog of claims awaiting adjudication by the VA is tarnishing the VA’s brand in the eyes of veterans, who see this backlog as a tangible expression of the government’s disdain for them,” the report said.

Manar, who worked for 30 years in the VA benefits system before moving to the VFW, estimates that it will take a “decades-long” effort to repair problems that have been decades in the making, caused by years of neglect, underfunding and obsolete computers.

In recent years, the VA has poured money and workers into the system, and completed unprecedented volumes of cases. But the numbers point to a Sisyphean task. In 2010, the VA completed a million claims for the first time in one year — but an additional 1.2 million were filed. In 2011, the VA completed 1 million more claims, but 1.3 million were filed.

Shinseki’s 2010 decision to allow more Agent Orange-related claims righted a wrong, veteran advocates say, but it also resulted in 260,000 new claims swamping the system.

There also has been a sharp growth in the average number of medical conditions for which each claimant files. World War II-era veterans submitted claims for one or two medical conditions, and Vietnam veterans three to four conditions. The newest generation files 9 to 11. About 45 percent of Iraq and Afghanistan veterans are seeking compensation for service-related injuries, a higher percentage than previous conflicts.

Hickey cites reforms that will answer “the million-claim question.”

In pilot program testing, the new paperless Veterans Benefits Management System has cut the average time to process a case from 240 to 119 days. The system is on track to be used nationwide by the end of 2013, Hickey said.

A long-awaited VA-Defense Department collaboration creating an Integrated Disability Evaluation System for members of the military returning to civilian life is showing promise, allowing the VA to award benefits on average within two months of discharge.

An “express lane” to speed claims for at-risk veterans is being tested, though veterans groups warn that the split has backed up other claims.

Employees who have completed a redesigned training program are processing 150 percent more claims, with a 30 percent increase in accuracy, Hickey said.

Veterans groups say that the “overpowering array” of pilot programs, initiatives and technological improvements make it difficult to determine which hold the most promise. And, they say, some of the VA’s 56 regional offices are resistant to the mandated changes.

“So many things cannot be fixed by sweeping decisions in Washington, D.C.,” said Peter Gaytan, executive director of the American Legion’s Washington office. “If the central office and General Hickey have a great idea, it’s only effective if the regional offices do it.”

Richard Dumancas, deputy director of benefits for the Legion, said morale is low at many regional offices, with employees overwhelmed by piles of documents a foot high or more for a single veteran.

“They want to help the veterans, but a six-foot pile, that’s pretty depressing,” he said.

It’s even harder for people like Lynn Callaway, a 58-year-old Air Force veteran who was awarded the Air Force commendation medal for her services during Operation Babylift, when children were airlifted from Vietnam before the fall of Saigon.

Callaway submitted a claim in 2005 for service-connected fibromyalgia, a disorder that causes pain and fatigue, but was denied benefits by the VA. She appealed the decision but it took six years to get a hearing before the Board of Veterans Appeals in January. The judge ruled in her favor and sent her claim to the Roanoke regional office in March to get a disability rating.

Callaway made no further progress for seven months. Her queries to Roanoke were met with form letters saying the case was being processed. In the meantime, she borrowed money from friends and relatives and has lived with a fellow veteran in Springfield to save rent. “I am tired. I am so tired,” she said Monday. “There has to be a better way. I’ve turned a little bitter in the last six months.”

The Washington Post asked the VA about Callaway’s case. On Thursday, an official with the Roanoke office said the case had been resolved and that she would soon receive her benefits.

“The years of waiting it takes for a claim to be sent to the appeals court with more years of waiting after the appeals decision can easily destroy veterans and their families,” Callaway said later. “This is unacceptable, and there should be great embarrassment within the administration that cases like mine exist.”