To the number of things Americans can do only in New York City – sip a true egg cream, have old-style seltzer bottles delivered to your door, easily secure a $2 shoe shine – add this: Get a sweater mended.

You and I may know the practice by the prosaic term of darning, and perhaps remember our grandmothers being adept at it. The people who do it professionally call themselves reweavers. And in today’s throwaway society, there are precious few of them left. Just a handful, by the reckoning of Ronald Moore, proprietor of the 75-year-old French American Reweaving Company.

In Manhattan he means, right? No: “That’s not just Manhattan,” he corrects with some urgency. “That’s the whole country!”

Because the other 49 states lack people in his trade, Mr. Moore’s custom goes far beyond the local – though he gets plenty of that. Packages stuffed with beloved garments arrive in the mail daily. A woman’s Armani suit from San Francisco. A camel hair coat from Chapel Hill, N.C. An overcoat from Franklin, Mich. The racks at French American Reweaving’s cramped offices drip with such orders.

“I’m so busy doing what I have to do, I’ve never had to worry about where the next customer is coming from. I’m not bragging. That’s the reality of the thing.” In other words, he has a thriving concern in a vanishing industry.

And therein lies the central irony of the reweavers’ world. The city’s few practitioners are doing bang-up business; yet, there’s little or no hope that fresh talent will soon step in to meet the demand. The key to this conundrum is held in a few dozen aged hands.

“There’s no one in this business under 60,” explained Mr. Moore who, perhaps thinking of a pressing rush job on a herringbone jacket with an L-shaped tear in the left elbow, talked very fast. “It’s a dying craft and they learned it a long time ago. It’s mainly women in this business and they started young, they picked up the practice. They learned it in Europe. There were all those mills over there at the time. Something would be damaged and they’d teach kids how to put threads in. From that, they perfected their skills.” Mr. Moore, who does not stitch himself but handles the business side of things, is a relative spring chicken: He’s 54.

“We’ve tried to train people in their late 20s or 30s,” he continued, “and they can never pick up the skill to a point where they’re very good at it. Some weaves are very basic, and they can pick those things up, but you have very complicated weaves in this business. The machines they have to day can do certain patterns that never could have been done before. They can give you patterns that are mind-boggling for a reweaver. It’s like looking at a set of hieroglyphics!”

Then there’s the problem of even getting young people interested in at a distinctly Old World occupation. “You have to have the desire to want to do it,” Mr. Moore contended. “Why would you? This is very labor intensive. You have to work at this. This is not a simple thing. You have to earn your money. If a kid is going to be a doctor, lawyer, or computer programmer, his mother and father are not going to tell them to become a reweaver!”

And so he must preserve the happiness of the few prized elderly ladies he employs. “They’re in big demand, so they call their price,” he said. Most were born in foreign lands where precise hand work was once taught. Italy. Cuba. France. Two Greek sisters are also on the payroll. Many – too old to get around easily – work from home, with a relative acting as conduit.

If you have a pair of injured trousers and seek sartorial redress, don’t hunt for a storefront. Look up. Reweavers, rare birds that they are, dwell on lofty perches. Mr. Moore’s offices hover 14 stories over West 57th Street. The 60-year-old Superior Weaving and Mending, run by Seymour and Morty Schnall, sits in a cubicle far from the elevator, 17 floors above a Starbucks off Union Square. Alice Zotta, a petite old woman with a thick Italian accent, works near the top of a tower at West 45th Street and Fifth Avenue. Ms. Zotta’s customers stand in a dingy, nondescript room that only a flatterer would call a vestibule. Clothes are handed through a small window; on the other side a hive of busy sewing bees buzz.

As a group, reweavers are of an odd, skittish character. Though chatty, they aren’t enthused by the idea of sitting down with a reporter. After a few phone calls, a journalist can feel like a beggar. “Who has time to gab?” is their unspoken question? “I’ve got a date with a needle.”

“Time is precious,” Mr. Moore said. “That’s the one thing that we have so little of in this business.”

Mr. Moore began his life at French American in 1967, when a friend who worked there said the company was looking for some part-time help. A teenager at the time, he stayed on and learned by observing. He credits his rise to the top to mainly being “in the right place at the right time.” About the company’s rather hoitytoity name, he explains: “The women who used to do the work were mainly from France. And Nathan Singer, who started the business in 1930, was an American guy. So they called it French American.”

A job typically takes weeks – not just because of the high number of orders, but due to the labor and time required to execute an assignment. Mr. Moore’s standards are as high as his address. “The question with us is if it’s going to look right. My reputation is more important than a few bucks. That’s part of who I am. I can’t not be fair with somebody. I’ve got to give you the best I can give you. And if I have to work over and do more time, I’ll do it. I want to make that as perfect as I possibly can.”

In his 38 years on the job, Mr. Moore has seen his services called upon by some high-toned types. Jazz legend Lionel Hampton sent in a salmon-colored sweater. Leonard Bernstein spent $125 to get his black cape repaired. And Mrs. Nelson Rockefeller sought help with a tear in a black print chiffon gown.

Yes, Mrs. Nelson Rockefeller. Even more unbelievably, Alice Zotta recently restored a pair of pants owned by George W. Bush. Sheesh. Can’t rich folks afford to simply buy something new? Mr. Moore broke into a pumpkin grin and laughed loudly the folly of the question. “People throw away their clothes and then wonder why they’re poor!”

It seems clear that people need Mr. Moore and his colleagues. Yet there’s no help for it: The trade is in its twilight. What will happen in the future when a coat cries to be whole again and there is no hand to heal it? “Oh, reweaving will be around,” he said, adopting an ameliorating tone. “But it will be so limited. They’ll be like the people who work in the Metropolitan Museum in art restoration. They’re so skilled and there are so few of them that they can charge you an arm and a leg.” At least, then, the President’s clothes are safe.