GAINESVILLE, Fla. — Jonathan Bey hurt his back while repairing buoys at sea in the Coast Guard, and after he was discharged, he filed what he thought would be a routine request for veterans disability benefits.

That was 34 years ago. After repeated denials by the Department of Veterans Affairs, appeals by Mr. Bey, and more than a couple of letters saying that the department had lost his files, Mr. Bey is still waiting.

“My adult life has been consumed trying to battle the bureaucracy,” said Mr. Bey, 61, who said he had to quit his civilian job 10 years ago as the injury grew worse. He now relies on his wife’s income and a steady supply of pain medication to get by.

The veterans benefits system started more than a century ago, and in the time since — as new wars stacked on entitlements and new abuses stacked on reforms — it has grown into an unruly tower of regulations. It pays out more than $ 78 billion each year to nearly five million beneficiaries. But there are also more than 470,000 veterans who have been denied benefits and have appealed. When they do, they encounter an antiquated system where processing cases takes years — and sometimes even decades.

“One of them,” Senator Johnny Isakson, chairman of the Veterans Affairs Committee, noted in a hearing this summer, has been waiting “25 years to get an answer.”

Actually, scores have been waiting that long, according to the department. Another 22 have been waiting more than 30 years. And wait times keep growing.

Recognizing the problem, Congress in August passed broad reforms to cut delays. President Trump quickly signed them into law, telling veterans gathered at the signing, “This is a big one.”

While veterans groups largely praised the move, critics said it would do little to help veterans already in the appeals system. That is true for Mr. Bey, who was recently told it would be at least another 14 months before he heard anything about his case.

“I hate to use a hackneyed expression, but they are rearranging the deck chairs and the ship is still sinking,” said John Wells, a retired Navy commander and lawyer who runs Military-Veterans Advocacy, a nonprofit.

The main cause of delays, according to the department, was a design flaw that fed appeals with simple errors into a legal system that was meant to rule on complex cases. That led to thousands of cases with issues as small as a typo clogging up the flow of cases to be processed.

“We tried to do everything in one stream and it couldn’t work efficiently,” said David McLenachen, who leads the department’s benefits appeals office.

The new law triages appeals into three streams: A fast stream — like the express lane at a supermarket — to correct simple errors; a medium stream, in which a more experienced department specialist reviews more complex issues at a local level; and a final stream where veterans can take cases to an independent board of appeals. The agency plans to hire hundreds of additional claims processors with the goal of clearing each case within four months.

But lawyers who represent veterans say the changes do not address the core problem: The department’s vast number of errors, which have generated hundreds of thousands of appeals. A 2017 report by the Government Accountability Office found nearly half of cases were plagued by mistakes and reached the Board of Veterans Appeals — the final authority for veterans benefits cases — only to be sent back for fixes.

Cases that have been sent back can sit for years before they are addressed, then sit again as they wait for the board to read the revisions.

Making a fair ruling on injuries of war is far from easy, and veterans advocates say some cases will inevitably take time to sort out. But as Mr. Bey’s case shows, even simple issues can languish, and recent changes by Congress have so far offered veterans like him no relief.

Mr. Bey was working with a crew scraping barnacles off buoys in Chesapeake Bay in 1977 when his ship suddenly listed to port, causing a shelf holding heavy equipment to tip. Mr. Bey braced himself against the equipment to protect crew members working below, and held it until others could help him. The next morning he turned to grab his duffel bag and collapsed in agony. “It was like a dentist’s drill, but in my back,” he recalled.

He spent four days in an Air Force hospital, military records show. They also reflect that during the five remaining years of his service, he was struck periodically by debilitating spasms.

But in 1983, when Mr. Bey submitted a claim to get free medical care and a small pension for his back from the Department of Veterans Affairs, the department sent back a letter saying it could find no evidence in his exit physical exam that showed the injury.

He appealed, asking that the department review his entire medical record. He was denied. He dug through the National Archives outside Washington, found records of his hospitalization, and submitted them. He was denied again. He got a civilian doctor to perform X-rays and write a letter documenting damage to his spine. He was denied again. He appealed to the Board of Veterans Appeals. His claim was denied.

Each denial was punctuated by months or years of delay as paperwork sat waiting. In the meantime, Mr. Bey worked as a researcher for an intellectual property law firm, got married and raised his children.

Because his claim had been denied, he was unable get medical care from a veterans hospital, and, he said, his back pain grew worse to the point that he was unable to work a full-time job.

“We see hundreds of cases like this,” said Bart Stichman, a lawyer and the joint executive director of National Veterans Legal Services Program, a nonprofit advocacy group. “One veteran with diabetes spent years trying to prove her case. She lost a foot. The V.A. finally granted the benefit, but by that time she’d lost her other foot.”

The veterans department said it was working to improve response time and reduce errors.

“The problem isn’t the process,” Mr. Bey said as he sifted through stacks of files showing agency errors in his case. “It’s that the quality of work is so bad. If people had done their job right, this would have been over in the Reagan administration.”

By 2016, Mr. Bey had exhausted all but his last appeal. He submitted the same evidence that had always led to a denial in the past, but, hoping to bolster his chances, sent it through the office of his senator, Bill Nelson of Florida.

A few months later, his benefit was granted — sort of. A department error in the date of the original claim erased decades of back pay. Mr. Bey is appealing. The department has told him it could take a while.