At a drop-in center for homeless youth, Mayor Eric Adams made a promise last year. By marshaling limited city resources and following a detailed blueprint, New York City would aim to eradicate homelessness among younger New Yorkers.

It was a bold goal, but one the mayor said was personal to him as someone who grew up on the brink of poverty and eviction.

But since Mr. Adams unveiled his plan, the administration has all but abandoned key elements of it. The charity that served as the host of his announcement went under, citing years of late payments from city government as a main reason. The mayor discontinued integral parts of the plan, leaving vacant a years-old City Hall position dedicated to tackling youth homelessness, and discontinuing the newly created “peer navigators” for homeless and runaway youth.

In his nearly two years as mayor, Mr. Adams has struggled to meet the city’s need for varied critical services, especially as other challenges arise. Some efforts, like ending youth homelessness, have suffered; other initiatives, like fighting crime and rats, have been more successful — helping fulfill the mayor’s campaign pledge to reduce visible signs of disorder.

Yet a comprehensive review of the Mayor’s Management Report, a 520-page compendium packed with statistics about the city’s performance during Mr. Adams’s tenure, shows that services elsewhere are sliding, and perhaps none more glaringly than those serving the city’s most disadvantaged residents.

In the recently released report, the city flagged numerous “critical indicators” to measure its agencies’ progress in areas of concern. Of the 65 indicators gauging progress at social services, slightly more than half had gotten worse, according to the report. Roughly a third showed improvement, and seven were stable.

For Mr. Adams, the challenges confronting the city have never been greater. More than three years after the coronavirus pandemic began, the city’s economy is still hampered by the work-from-home trend, and now the administration must deal with the financial implications of a migrant influx that shows no sign of abating — complicating efforts to improve the city’s delivery of certain social services.

Only 40 percent of applications for food stamps were processed within a month, the legally mandated time frame, compared with 60 percent the year before and 93 percent before the pandemic.

Though the city reduced the time it takes to fix more systemic heat outages, it has been taking longer to address individual emergency heating and hot water requests in public housing, home to roughly 400,000 New Yorkers. It is taking significantly longer to prepare vacant public housing apartments for new residents, even as homelessness soars.

In Mr. Adams’s first full fiscal year as mayor, his administration took more than twice as long to process rent-freeze requests from low-income seniors and disabled New Yorkers, a problem the city blamed partly on budget-related staffing shortages. Even police response times rose across the board.

Jonah Allon, a spokesman for Mr. Adams, said the mayor remains focused on helping low-income New Yorkers, and pointed to areas where the administration made gains.

In a statement, Mr. Allon said that the administration had “built the most supportive housing units in a single year in the city’s history, paired more foster youth with life coaches through the Fair Futures program, increased the number of families accessing child care through vouchers by roughly 73 percent and so much more.”

“Weaving a robust social safety net is a core component of Mayor Adams’s ‘Working People’s Agenda’ for a more equitable city,” Mr. Allon added.

Indeed, the city moved more homeless households into new housing, and increased the number of summer jobs and internships available to young New Yorkers and the number of seats available in Summer Rising, a summer school and recreational program created during the pandemic.

Yet many vulnerable New Yorkers struggle each day because of gaps in city services.

Stephanie Johnson, a single mother of four, was at risk of losing her Brooklyn home after her landlord abruptly stopped receiving rental subsidies from the city. Another mother in Brooklyn, Diana Cruz, was facing eviction and did not have a lawyer to help her, even though a city law guarantees free legal assistance.

In the Bronx, Diana Ramos was struggling to find her next meal after the city took weeks to approve her request for food stamps. When Ms. Ramos, 46, called the city’s Human Resources Administration for help, she waited on hold for hours to no avail. She ended up relying on food pantries and her father, who recently sent her $40 over PayPal to buy some basics.

“I’m a diabetic,” she said. “It’s not like I can buy a big box of ramen noodles. I need vegetables. I need protein.”

Ms. Ramos, who was assisted by the Safety Net Project at the Urban Justice Center, said she was relieved when her food stamps arrived last week, the day after The New York Times asked city officials to comment on her case.

“You know that I qualify for food stamps — I have no income,” she said. “Why is this so hard?”

A confluence of factors has contributed to the recent decline in city services.

The mayor has forced city agencies to curb spending, over the objections of Democrats on the City Council, citing an uncertain economic outlook and new labor deals. He has warned that additional budget cuts and a hiring freeze might be necessary as the city struggles to pay for housing thousands of migrants arriving from the southern border. The proposed cuts of up to 15 percent over the next year would be much deeper than past cuts and could prove even more harmful to poor New Yorkers.

Policy differences between Mr. Adams and his predecessor, Bill de Blasio, have also led to cuts for some of the previous administration’s priorities, including prekindergarten for all 3-year-olds.

Even before the migrant crisis, a city worker staffing shortage had hollowed out agencies; with more than 26,000 vacant positions, the city has found it difficult to deliver some basic municipal services, especially in a timely manner. This summer, nearly 7 percent of full-time city government jobs were unfilled, compared with around 2.5 percent in 2020, 2019 and 2014, according to the Citizens Budget Commission.

Mr. Allon acknowledged that “the ongoing asylum seeker crisis” has had “significant impacts on our city’s budget and agency operations.”

Demand has surged for cash assistance in New York City, yet 6 percent of the jobs are unfilled at the city division responsible for dispensing public assistance — more than double citywide historic norms, according to data provided by the state comptroller’s office.

The city processed only 29 percent of applications for cash assistance on time, compared with 95 percent in 2019. The delays violate state and federal law, a federal judge in Manhattan recently ruled, and the city must figure out a path to compliance by early next year.

Phara Souffrant Forrest, a state assemblywoman from Brooklyn, called the delays “shocking and cruel beyond words.”

Some agencies have taken months to fill important positions — a situation that some critics believe is a strategy by the Adams administration to lower costs.

Interviews with 13 current city staffers suggest that while the situation has improved this year at some agencies, others are still short-staffed, and triage remains the norm.

Last summer, city officials wrote a letter to the mayor’s office warning that low staffing levels were threatening critical services. The city budget office took 17 months to approve the hiring of an essential staff member, which prompted the director overseeing that position and members of the team to resign in protest, according to the letter, which was obtained by The Times.

The 11-page letter listed dozens of examples where services were endangered or harmed: A health center in Harlem delayed a distribution of cribs and car seats to families that is part of an effort to reduce infant mortality; there were fewer lead inspections at homes with newborns where other building units had documented lead paint hazards; a program that provides free eye exams to kindergartners and first-grade students reached 15 percent of eligible students, compared with 95 percent in the 2019-20 school year.

The staffing shortage also affected the city’s highly respected sexual health clinics and tuberculosis clinics. They have not fully reopened since closing at the height of the pandemic, even as sexually transmitted infections are rising and there are growing concerns about tuberculosis.

The city’s eight sexual health clinics saw nearly 95,000 annual visits before the pandemic; that number has dropped to nearly 62,000 over the last year, according to data from the Health Department. Only five of the clinics offered sexual health services, and a sixth reopened in July.

As for tuberculosis — a highly infectious disease that has higher rates in some other countries from which people emigrate to New York — one of the city’s four clinics, in Washington Heights, closed as part of the pandemic response and has not reopened.

Dr. Jay Varma, who served as a top health adviser to Mr. de Blasio, called on the city to reopen all the clinics. “They’re really a true safety net facility,” he said.

The declines in service are not limited to those for struggling New Yorkers. A lifeguard shortage prompted pool closings this summer. The Department of Cultural Affairs, which supports cultural institutions across the city, is responding to only 28 percent of customer service emails within two weeks, less than last year, and down from 91 percent in 2019. New York City installed fewer protected bike lanes and fewer bus lanes than the year before, and the city appears to be on track to install fewer than legally required this calendar year. The number of street trees pruned fell to 46,000, roughly the same as last year and compared with nearly 71,000 in 2019.

“There are a lot of nuts and bolts that seem to be loosening,” said Andrew Rein, president of the Citizens Budget Commission.

With the migrant crisis overwhelming the city’s shelter system, the threat of homelessness is particularly troubling.

Ms. Cruz, 43, who lives in the Bronx and has nine children, is fighting eviction in housing court, but has not been able to secure a lawyer through the city’s right to counsel law. The law provides free access to lawyers for tenants in eviction cases, but there are not enough lawyers available.

Ms. Cruz’s circumstances are hardly unique: As eviction cases have risen sharply, 63 percent of tenants facing eviction had legal representation during a three-month period last year — down from 71 percent during the same period in 2021, according to the city’s Office of Civil Justice.

“This is my first eviction,” Ms. Cruz said. “I’ve always paid my rent. I don’t know what to do. I don’t know where to start.”

A year ago, Lyndon Chris Hernandez, a 26-year-old formerly homeless man who has emerged as a leader in the world of homeless and runaway youth, appeared with Mr. Adams at the unveiling of the mayor’s plan to end youth homelessness. Mr. Hernandez got a job as a privately funded peer navigator for runaway and homeless youth, but saw his colleagues who were hired with city money lose their jobs.

In August, over breakfast at a diner in Queens, he said he was not all that surprised by the administration’s actions. “The mayor makes empty promises,” he said.