The paperwork stacks up slowly but steadily.

Some months, the pile of appeals from insurance companies denying coverage of a medical implant for severe acid reflux is more than a foot high in Minneapolis surgeon Dr. Dan Dunn’s office. Such appeals take months or years to resolve, and may still end in denial even though the government has approved the device.

“We had, at one point, 40 patients,” Dunn said, describing appeals for coverage denials for the Linx, an implantable device that controls acid-reflux and is made by the Shoreview medical device company Torax Medical Inc.

Commercial insurance companies are demanding more evidence than ever about medical devices before granting coverage. Commercial approval from the Food and Drug Administration, once seen as the light at the end of the tunnel, today signals the start of a longer journey toward mainstream acceptance for some novel devices.

The Linx is a string of titanium-wrapped magnets that rings the lower esophagus to keep down food, bile and stomach acid. It was unanimously approved by the FDA three years ago, and Medicare covers it today. The company is presenting the latest analysis from a clinical study following Linx patients for five years post-implant on Monday.

But most commercial insurers still see the Linx as too new to cover. Spokespeople with Aetna and Blue Cross and Blue Shield of Minnesota said they consider the device “investigational,” needing further study.

That leaves most people whose doctors recommend the device to file appeals, often without success.

“The reality is, devices add cost. They don’t subtract cost,” said Dr. Archelle Georgiou, a Twin Cities health care consultant and former chief medical officer at for-profit insurance giant UnitedHealth Group Inc. in Minnetonka. Although devicemakers say their products justify added costs by reducing other long-term expenses, “that has rarely come to fruition,” she said.

Device proponents argue that insurance companies’ reluctance to adopt coverage for Linx has crossed the line between protecting patients from unproven technology and limiting access to an accepted therapy.

“The frustrating part is for the patient,” said Todd Berg, co-founder and CEO of Torax. Coverage denials are “confusing to patients, because they assumed that if their physician recommends it and it is medically necessary and FDA-approved, that it’s a covered benefit. And it isn’t.”

The stalemate has left Torax Medical to pursue unorthodox strategies to get its devices to patients, including appealing to health care ­providers directly.

Earlier this year, major Twin Cities health system Allina Health added coverage of the Linx to its self-insurance plan, which counts 26,000 Allina employees and their families as members. Allina became the 10th self-insured health care provider nationally to add coverage for their own workers — even as hospital patients on commercial insurance struggle to access it.

The Allina decision was a particularly satisfying development for Torax, because the health system includes south Minneapolis’ Abbott Northwestern Hospital, where Dunn performed the first Linx implant in 2007. Abbott’s gastroenterology chief, Dr. Robert Ganz, helped develop the device and has published papers supporting its use.

“We are a place that feels like innovation is part of what we do, and I want to be supportive of our doctors, when I can, to do that,” Abbott Northwestern President Dr. Ben Bache-Wiig said in an interview about why he advocated for the system’s health plan to cover the device.

Bache-Wiig said it wasn’t surprising to see the Linx find trouble gaining traction among commercial insurers like Aetna and Blue Cross, especially when other ­treatments for acid reflux exist. “Insurers in the last few years have been trying to be very conservative about adopting new technologies, and I don’t think this device is unique in being FDA-approved but not getting wider payer acceptance,” he said.

Acid reflux happens when a small ring of muscle near the base of esophagus fails to contract tightly enough to keep the stomach’s contents from leaching up toward the throat. Severe forms of gastroesophageal reflux disease (GERD) can lead to chronic heartburn and disrupted sleep. Injuries to the esophageal lining from GERD in a fraction of patients are associated with a condition called Barrett’s esophagus, which increases cancer risk.

Acid reflux is one of the most common medical problems in America. There is no shortage of pills to treat it, including “proton-pump inhibitors” like Nexium and Prilosec that cause the stomach to make less acid.

For reflux that can’t be controlled with drugs, the surgical treatment covered by all the major insurers is a Nissen fundoplication, in which a section of the stomach is dissected and wrapped around the esophagus like a hot dog bun to reinforce the existing muscle.

The Linx is an alternative. The device consists of a string of titanium-wrapped magnetic beads whose attraction is precisely calibrated to give way when food is passing down the esophagus, or when burps and vomit are traveling up. Doctors say it can be a better therapy for Linx-eligible patients for whom Nissens leave them unable to vomit or burp properly.

Dunn said about 4 percent of patients with a Linx device get it removed because they have difficulty swallowing. He compared that to the rate of revision surgeries for Nissen procedures with difficulty swallowing, which runs between 7 and 10 percent, Dunn said.

Prices for GERD interventions are fairly modest. Bache-Wiig said a Nissen costs between $3,000 and $5,000 at Abbott. A Linx procedure costs roughly $1,500 more, and “almost all of that differential is the cost of the device,” he said.

Dunn noted that Nissens require an overnight hospital stay, while the majority of Linx procedures are done as day surgery, which should cut down on overall hospital costs.

A safety analysis of the first 1,000 patients who got Linx devices, published this month in the journal Diseases of the Esophagus, found that 1.3 percent of patients were readmitted and 3.4 percent had re-operations to remove the device. Another study found 86 percent of patients eliminated daily dependence on acid-reflux drugs after getting a Linx.

Insurers want more. Aetna spokesman Rohan Hutchings wrote in an e-mail that Linx “has not been established as an effective option.”

Torax executives revealed that they have recently partnered with Blue Cross affiliate Highmark to assess the Linx’s cost-effectiveness.

Doctors who support the procedure will be watching closely to see how insurers treat the new data. “I think they’re going to have a hard time denying it now,” Dunn said. “But they just say they don’t want to pay. Who can make them?”