Nineteen-year-old Lynette Santiago, a housekeeper in the Environmental Services Department of Yale-New Haven Hospital, met him while grabbing coffee at Dunkin’ Donuts six months ago.

The man was dressed in a union uniform, she recalled — the New England Healthcare Employees Union District 1199, Services Employees International Union. She took his card. (“I didn’t keep it,” she said.) They have not seen each other since.

Santiago, a relatively new employee, was not around to see the effort that SEIU/1199 undertook a decade ago, when an effort to unionize hospital workers sparked a conflict between union organizers and hospital officials. When the hospital interfered with organizers’ efforts to have a union election, Yale and City Hall officials intervened, and an independent arbitrator slapped hospital officials with a $4.2 million penalty, $2 million of which was given directly to the union.

Union spokesman Bill Meyerson said at the time that the money would be used to continue the unionization effort. But, one year on, there has been no progress. Each of the 28 hospital workers interviewed this month said SEIU/1199’s unionization effort has been all but silenced. Although SEIU/1199 officials said the effort continues, employees have been noticing ever fewer organizers out on campus. And words like “SEIU,” “1199” or “unionize” have disappeared from the lexicon.

“The campaign is shifted to a rather — what’s the best way to describe it? — less visible effort,” Meyerson said in an interview this week.

Although he said the unionization effort was still active, the union spokesman declined to speak about the details of the strategy. It would “alert the employer of our plans,” Meyerson said.

But Yale-New Haven Hospital Senior Vice President for Public Affairs Vin Petrini said the hospital administration is not at all concerned with the “union issue.”

“We’re focusing on making sure that our employees feel valued,” he said.

Indeed, Elancy Cromwell, a 20-year-old housekeeper at the hospital, said she does not believe giving the union $2 million was good use of money: “If nobody wants to be in a union, then the money should be used for something else instead of wasting it,” she said.

Meyerson said Wednesday that the money has been used to pay union organizers and allow the union to start a public education campaign, if and when they choose to conduct one. No such campaign exists at the moment, he added.

This diminished effort appears to be part of a growing trend: Across the United States, workers seem to be less active in pushing for unionization. Over the last 12 months, the National Labor Relations Board received 33 percent fewer petitions for unionization than it received the year before, said J. Justin Wilson, managing director of the pro–right-to-work Center for Union Facts.

One potential reason, he said, is that the union officials are awaiting the passage of the Employee Free Choice Act, a piece of legislation that would force employers to recognize workers who sign up for a registration card as a union member. Another reason, he added, is diminishing returns.

“It costs money to mount these campaigns,” Wilson said. “It cost man-hours and costs other things. … Unions are not insane.”

“Of course, they never give up,” he added. “It’s really rare that a union never returns that is trying to unionize a company.”

SEIU/1199 may buck the trend, however. For many months, a union organizer had set up shop in Dunkin’ Donuts at 51 York St., store manager Agnieszka el Yakine said. He waited by the store for three to four hours, four days a week, the manager said, wearing purple or yellow (the union colors) and meeting with workers about the union.

“He’s like a regular, like other people,” he said. “He comes, sits down and drinks coffee.”

But Dunkin’ Donuts employees said that recently, after many months of campaigning, the man had stopped coming to the store. Managers of nearby stores said they have never seen organizers waiting by their premises. And Petrini said he was not aware of any organizers at the hospital.

Still, Meyerson said the hospital “is a big place. There’s lots of places for us to [organize].” He declined to say to where the organizers have moved.

“There’s not a whole lot to report,” he said.