They seemed to be getting close to a solution. But now General Electric, the company that developed a technology for carrying it out, has quietly dropped work on the project, saying it is not commercially viable.

The isotope is technetium 99m, or tech 99 for short. It is useful in diagnostic tests because it throws off an easy-to-detect gamma ray; also, because it breaks down very quickly, it gives only a small dose of radiation to the patient.

But the recipe for tech 99 requires another isotope, molybdenum 99, that is now made in nuclear reactors using weapon-grade uranium. In May 2009, a Canadian reactor that makes most of the North American supply of moly 99 was shut because of a safety problem. A second reactor, in the Netherlands, was simultaneously closed for repairs.

The 54-year-old Canadian reactor, Chalk River in Ontario, is running now, but its license expires in four years. Canada built two replacement reactors, but even though they turned out to be unusable, their construction discouraged potential competitors.

So the United States Energy Department, which regulates nuclear weapons, has been trying to find a way to make the molybdenum isotope without relying on leaky reactors that use bomb fuel. And in 2010 General Electric, which designs power reactors, came up with an innovative solution.

The commercial reactors have a big flow of neutrons, and if an atom of natural molybdenum absorbs one, it becomes moly 99.

G.E.’s reactors have an opening at the bottom for an instrument that measures the neutron density. The company said it could replace that monitor with a “target” made of molybdenum and pull it back out after about seven days, so it could be sent to a chemical processing plant for recovery of the moly 99.

The company even picked out a reactor, Exelon’s Clinton plant in DeWitt County, Ill. And it lined up industrial partners for the parts of the process it would not do itself, and tested the concept in research reactors.

There is a drawback, though. Only about 24 percent of natural molybdenum is moly 98, the kind that can be converted to moly 99. To produce a given volume of tech 99, the volume of molybdenum in the generator has to be far larger.

Enter another player: Perma-Fix, a company based in Atlanta that makes a resin for treating contaminants at polluted industrial sites.

The company came up with a resin that will hold the atom when it is molybdenum but release it when it decomposes into technetium. Perma-Fix executives say this is a good complement to the G.E. system.

But G.E. has given up. When the Canadian reactor was restarted, it said, it decided that its technology was not financially competitive. In a statement, G.E. said that while it and Exelon were confident “that large quantities of molybdenum 99 could safely be produced” in one of their reactors, financial projections “do not support the remaining cost.”

Kevin Walsh, a nuclear-fuel executive at General Electric, said that the company would finish developing the system if the economics improved but that for now, “we’ve put all the engineering aside.”

Louis Centofanti, chairman and chief executive of Perma-Fix, said his company was trying to line up other reactors to process the molybdenum. Federal officials say Perma-Fix may have a time advantage, because it is not using government money and thus does not have to file an environmental impact statement.

But experts say it may be nearly impossible to develop an alternative supply while highly enriched uranium is still in use, even though the reactors that do that work have an uncertain lifetime. Chalk River’s license expired last year, but it was given a single five-year extension; the Dutch reactor’s lifetime is less certain but also limited.

“The economics is key,” said Parrish Staples, director of European and African threat reduction at the National Nuclear Security Administration, who has been meeting with European officials looking for ways to stop using highly enriched uranium. The old, unreliable reactors now in use are subsidized by government, he said.

His agency backed G.E. but also a number of other companies. One, NorthStar Medical Radioisotopes, uses an accelerator to create gamma rays that bombard yet another type of molybdenum, moly 100; the bombardment causes the substance to eject a neutron and become moly 99.

Another organization, the Morgridge Institute for Research in Wisconsin, uses an accelerator to bombard uranium in a liquid solution, but it uses uranium with a much lower content of uranium 235, the kind that is useful in bombs.

And the Energy Department is helping finance a research program at Babcock & Wilcox to develop a new kind of reactor, in which uranium will be circulated in a liquid, and split; fission products, including the desired type of molybdenum, will be filtered out of the liquid for medical use.

Dr. Andrew J. Einstein, an assistant professor of clinical medicine at the Columbia University College of Physicians and Surgeons, who testified before a Senate committee in 2008 about the isotope shortage, said supplies were adequate at the moment.

But he drew a biblical analogy. “This is the seven years of plenty,” he said. “It certainly is time to be preparing for supply beyond Chalk River.”

Dr. Einstein said that when tech 99 was not available, doctors could use substitutes, but that these gave the patient larger radiation doses or provided poorer image quality to the doctor.

And for some uses, doctors can substitute PET scans, he said. But the equipment is in high demand for other procedures, and many medical facilities do not have it.