Earlier this summer, Trump administration officials hailed a new strategy for catching coronavirus infections: pooled testing.

The decades-old approach combines samples from multiple people to save time and precious testing supplies. Federal health officials like Dr. Anthony S. Fauci and Adm. Brett Giroir said pooling would allow for constant surveillance of large sectors of the community, and said they hoped it would be up and running nationwide by the time students returned to school.

But now, when the nation desperately needs more coronavirus tests to get a handle on the virus’s spread, this efficient approach has become worthless in many places, in part because there are simply too many cases to catch.

Pooled testing only works when the vast majority of batches test negative. If the proportion of positives is too high, more pools come up positive — requiring each individual sample to then be retested, wasting precious chemicals.

Nebraska’s state public health laboratory, for example, was a pooling trailblazer when it began combining five samples a test in mid-March, cutting the number of necessary tests by about half.

But the lab was forced to halt its streak on April 27, when local positivity rates — the proportion of tests that turn up positive — surged past 10 percent. With that many positives, there was little benefit in pooling.

“It’s definitely frustrating,” said Dr. Baha Abdalhamid, the assistant director of the laboratory. In combination with physical distancing and mask-wearing, pooling could have helped keep the virus in check, he added. But the pooling window, for now, has slammed shut.

Some laboratories have set their pooling thresholds even lower than a 10 percent positivity rate, effectively walling themselves off from the strategy as cases continue to climb by the thousands per week in most states.

Even in places where positivity rates are low, pooling isn’t always the best testing option. Deployed under the wrong circumstances, the strategy could actually exacerbate lab supply shortages and testing delays, experts said.

“A lot of us are still in the evaluation stage, trying to figure out what problems this will solve,” said Rachael Liesman, director of clinical microbiology at University of Kansas Medical Center, which processes several thousand coronavirus tests a week, but has yet to bring pooling online. “But it could create new problems, too.”

Despite relatively widespread acceptance in countries like Israel, Germany, South Korea and China, pooling’s rise to prominence in the United States has been sluggish. It wasn’t until July 18 that Quest Diagnostics became the first commercial lab to receive emergency authorization for pooled testing from the Food and Drug Administration. Since then, Quest has deployed its approach — which batches four samples at a time — in three of its labs, in California, Massachusetts and Virginia, with plans to roll out more on an undisclosed timeline, according to a company representative.

Another large testing company, LabCorp, was given the go-ahead on pooling on July 25, but has yet to debut the procedure in any of its facilities.

Certain hospital systems have also received emergency approval from the F.D.A. to run pooled tests. UC San Diego Health, for example, can run pools of five samples on a machine made by the pharmaceutical company Roche, and will likely receive clearance for two more in the coming weeks, according to Dr. David Pride, director of the health system’s molecular microbiology lab.

The strategy has already made significant headway in some parts of the country. In New York, where test positivity rates have held at or below 1 percent since June, universities, hospitals, private companies and public health labs are using the technique in a variety of settings, often to catch people who aren’t feeling sick, said Gareth Rhodes, an aide to Gov. Andrew Cuomo and a member of his virus response team. Last week, the State University of New York was cleared to start combining up to 25 samples at once.

At Poplar Healthcare, a lab services company based in Memphis, a team led by James Sweeney, its chief executive, is pooling several thousand samples each week. By batching up to seven samples, Poplar is now funneling crucial intel back to schools, fire departments and more, Mr. Sweeney said. In a lot of these groups, coronavirus positivity rates are below 1 percent, he added.

Pooling accounts for about one-third of the samples that are processed at Poplar, Mr. Sweeney said, adding “that percentage is going to get much higher.”

But in many other regions, experts are having trouble clearing the hurdles to benefit from pooling — in part because needs differ so vastly from institution to institution, and even from test to test.

“There’s been a lot of concerns about all the challenges,” said Dr. Bobbi Pritt, director of the clinical parasitology laboratory at Mayo Clinic, which processes tens of thousands of coronavirus tests each week, but has yet to roll out pooling.

Experts disagree, for instance, on the cutoff at which pooling stops being useful. The Centers for Disease Control and Prevention’s coronavirus test, which is used by most public health laboratories in the United States, stipulates that pooling shouldn’t be used when positivity rates exceed 10 percent. But at Mayo Clinic, “we’d have to start to question it once prevalence goes above 2 percent, definitely above 5 percent,” Dr. Pritt said.

And prevalence isn’t the only factor at play. The more individual samples grouped, the more efficient the process gets. But at some point, pooling’s perks hit an inflection point: A positive specimen can only get diluted so much before the coronavirus becomes undetectable. That means pooling will miss some people who harbor very low amounts of the virus.

“Are we going to cause harm if we miss them? I think that’s still a difficult question to answer,” Dr. Liesman said. These people may be less likely to pass the virus to others, and may be at lower risk of getting severely ill. But that’s no guarantee. Some might simply be early on in their infection.

Pooling can also be onerous for lab technicians — many of whom have been working grueling hours for months on end. Though simple in theory, batching samples is tedious and time-consuming, as researchers carefully transfer precise amounts of liquid from one tube to another hundreds, perhaps thousands, of times over.

“We’ve really been struggling in the lab already from repetitive use injuries,” Dr. Liesman said. Adding pooling to a lab’s repertoire, she said, has the potential to exacerbate that toll. “Pooling could help us do more tests with fewer reagents,” or chemicals, she said. “But if one of your issues is staffing, this doesn’t really help us at all.”

Retesting positive pools also requires a large database of samples so that each member of the pool can be identified and cross-checked. And any sort of mislabeling errors, or cross-contamination between samples, could disrupt the entire workflow and risk an incorrect result.

Robots called liquid handlers, which can automatically batch samples, could be a game-changer for many labs. But given the current testing crisis, many of these pooling-capable machines are in extraordinarily high demand. At UC San Diego Health, Dr. Pride’s team has been waiting about two months for the arrival of three new liquid handling instruments. One finally arrived on Monday.

To circumvent some of the issues, experts from disparate fields are cobbling together a few technical tricks. For example, in states, cities or even neighborhoods where coronavirus prevalence rates are high, less-hard-hit populations — “cold spots” — can still be plucked out and pooled, Dr. Abdalhamid said.

When applied to existing social groups, pooling could also help with contact tracing. As children return to schools, for instance, entire classrooms could be tested together. Any pools that come up positive could prompt immediate isolation for everyone involved, with swift, individual testing afterward, Dr. Christina Kong, medical director of the Pathology and Clinical Laboratory for Stanford Health Care, said in an email.

Massaged to fit each laboratory’s specific needs, pooling could still prove immensely useful for a large swath of the community, said Daniel Lakeland, who is partnering with researcher Hadi Meidani to develop a pooling “consulting” service. The two eventually hope to roll out a model that can crunch local prevalence numbers and a few other factors, then advise organizations on how to set up their pools. Depending on the circumstances, some pools might even be able to accommodate dozens of specimens at once.

But until those solutions are in hand, researchers are making do as best they can.

Every week, Dr. Abdalhamid of Nebraska’s public health lab checks the numbers, hoping for a sustained decline in local coronavirus cases. For months, the region’s positivity rate has stubbornly held around 20 percent.

But Dr. Abdalhamid hasn’t yet given up, he said: “Hopefully, when it hits 10 or below, we’ll get back to pooling right away.”