Residents pass through a security checkpoint at the Districts’ homeless shelter in what once was D.C. General hospital on February, 11, 2013 in Washington, D.C. (Bill O'Leary/The Washington Post)

This winter, the District’s shelter for homeless families at D.C. General Hospital is crammed full — 372 adults and nearly 600 children living in small, converted rooms, enough kids to populate an elementary school.

The ghostly old hospital complex on the city’s eastern edge has become a symbol of the intractability of family homelessness in the District — a problem that has persisted long after the recession ended and even as the housing market stabilizes.

The reasons it has proved so difficult to solve are in dispute.

City officials say that hard times and the lack of affordable housing in poor neighborhoods are to blame for the continuing crisis of family homelessness in the District, where the number of families on the streets shot up 18 percent last year alone — and 74 percent since the recession. Officials say they are making some strides in combating homelessness overall, buoyed by $4 million in rental vouchers for low-cost apartments and a $ 10 million increase in spending on homeless services.

But advocates counter that the city is not doing nearly enough to help the neediest residents find permanent housing at a time of budget surplus — and in some cases has been hindering families’ efforts over the past year to find temporary relief in its overflowing shelter system.

“It’s like paperwork on top of paperwork — they have to prove they absolutely don’t have a safe place to stay,” said Marta Beresin, a staff attorney for the Washington Legal Clinic for the Homeless, which issued a report on the city’s practices last week.

Saying the city was “increasingly in danger of becoming a city of only ‘haves,’ ” Mayor Vincent C. Gray (D) recently announced that he is slating $100 million for affordable housing to preserve or build some 10,000 units for seniors and low-income residents. But the units may be insufficiently subsidized to help the poorest residents, according to an analysis by the D.C. Fiscal Policy Institute.

D.C. Council member Jim Graham (D-Ward 1) said he thinks the city should find a way to use some of its $417 million budget surplus to aid its needy residents. Gray’s administration says that money is legally mandated to go into the general fund, or its reserves, meaning it can’t be used to provide more housing vouchers or other homeless services.

“The D.C. government is flush with cash . . . but some of what we’re providing is like third-world conditions,” Graham said. “Is it a warm bed? Yes. Is it out of the elements? Yes. But the fact of the matter is the quality of our homeless services is not high.”

Graham said Monday that he would hold a hearing on conditions at the D.C. General shelter Feb. 28.

In part because of its efforts to curb the problem, the city has had to put up fewer families this year in another temporary venue, motels along New York Avenue. It has used them to house about 50 families this winter vs. about 200 last winter, which cost the city $3 million. (The city, by law, must house residents when the temperature drops below freezing and has to use hotels when regular shelters are full.)

Advocates and homeless mothers with children complained last year of several instances in which mothers were told by shelter officials that they risked a child welfare investigation because they had no safe place to sleep. They said that the city instituted a new assessment system that requires families to fill out a burdensome amount of paperwork before they are admitted to shelters and that city officials sometimes wait until late in the evening to decide whether it is too cold to sleep outside, leaving some families on the streets.

David A. Berns, director of the Department of Human Services, said the city was merely trying to do a more thorough job of finding its homeless residents the right place to stay.

“What we’re trying to do through our new approach is take the resources we have and invest in what families tell us they want and need — which is enhanced housing opportunities and job training so they can afford housing on their own,” Berns said. The city is trying to “hold the number of people we have to put in shelters down to those where there is really no other alternative.”

Meanwhile, at D.C. General, parents report struggling to bathe their kids as they stand in chilly showers and to feed them lunches beyond microwave fare. Outside a few activity rooms, there is no real place to play. For a few weeks last month, the heat went out in some rooms, and there weren’t enough cribs for all the babies.

“It’s like rock bottom for me,” said Angel Jones, who at 21 has no family to speak of. She ended up in the city’s family shelter about a month ago with her daughter, Makiya, 4. “I’m tired of seeing four walls,” Jones said. “It’s like I’m in prison or something.”

On weekends and in the evenings, children run noisily around the industrial-looking halls of the abandoned hospital, which was shuttered in 2001. Volunteers from the nonprofit Homeless Children’s Playtime Project come a couple of times a week to do activities with the young children, otherwise there is little for them to do. There is no playground; the children play ball on the patchy grass near the bus stop.

Even basic parenting tasks can be a challenge. One young mother agonized about how hard it was to give an infant a bath in a shower and worrying the child might slip.

Others say they struggle to find healthy food for their kids for lunch, because residents aren’t allowed to cook or bring any food in that’s not microwaveable and end up relying on ravioli or ramen noodles. The shelter’s $300,000 lunch budget was cut last year, but it still provides breakfast and dinner.

For the older children, there are two computer rooms, but the equipment is often broken.

“I’ve got four in school, and they do their homework lying on their beds. There’s no tables, no desks, no nothing,” said Chante Walker, 37, a mother of five who came to the shelter in October. “I just think about getting out of here.”

Privacy is always an issue. Walker has a large room, for example, but shares it with all her children.

“It’s stressful, it’s real stressful,” she said. “Some days I literally sit in the room and my kids are asleep and I’m sitting and just watching them, feeling . . . I just feel displaced. My kids feel displaced.”

James Arkin and Eddy J. Palanzo contributed to this report.