U.S. cities struggling with soaring housing costs have found some success in lowering rents this year, but that relief has not reached the renters most at risk of losing their housing.Nationally, the pace of rent increases is beginning to slow down, with the average rent in at least six cities falling since last summer, according to Zillow data.But the decline is being driven primarily by decreasing prices for high-end rentals. People in low-end housing, the apartments and other units that house working-class residents, are still paying more than ever.Since last summer, rents have fallen for the highest earners while increasing for the poorest in San Francisco, Atlanta, Nashville, Chicago, Philadelphia, Denver, Pittsburgh, Portland and Washington, D.C., among other cities. In several other metro areas - including Los Angeles, Las Vegas, Houston and Miami - rents have risen for the poor and the rich alike.The ongoing increase in prices for low-end renters poses a challenge for city officials who have vowed to lower housing costs for working-class residents already struggling with tepid wage growth in the U.S. economy.City officials have said that a boom in luxury housing construction would cause rents to fall for everyone else, arguing that creating new units for those at the top would ease competition for cheaper properties.In part based on that theory, cities have approved thousands of new luxury units over the past several years, hoping to check high rents that have led more than 20 million American renters to be classified as "cost burdened," defined as spending more than 30 percent of one's incomes on housing.But although some advocates say the dividends could still pay off for low-income renters, others say more direct government action is needed to prevent poor residents from being forced out of their cities or into homelessness. They have called for the federal government to help construct more affordable units, or offer greater rental assistance for poor families."For-profit developers have predominantly built for the luxury and higher end of the market, leaving a glut of overpriced apartments in some cities," said Diane Yentel, president and chief executive of the National Low Income Housing Coalition, an advocacy group. "Some decision-makers believed this would 'filter down' to the lowest income people, but it clearly will not meet their needs."Poorer city residents have experienced significant rent increases over the past several years. In Portland, average rents for the poor have risen from about $1,100 to $1,600 - or by more than 40 percent - since 2011.In San Francisco, the average rent at the bottom of the market has soared from $1,700 to $2,600, a nearly 50 percent increase. Seattle's poor have also had their rents rise by close to 40 percent. Nationwide, rents for those at the bottom have increased by 18 percent.Rising rents for the poor threaten to add to the nation's homeless population, and put an additional severe strain on tens of millions of families, often forcing them to forgo other basic needs to avoid losing their housing.Construction in most U.S. cities came to a standstill during the Great Recession, amid a broader collapse in the housing market. As the economic recovery took off, its gains were disproportionately concentrated in a handful of cities, leading renters to move in droves to already densely populated urban areas.There was not enough housing there to greet them. By the early 2010s, rents in major cities were beginning to increase by more than 10 percent annually. Several cities declared emergencies over their rising homeless populations.In the following years, protracted battles have occurred in city halls nationwide over the size and makeup of urban communities, often pitting longtime homeowners trying to preserve the value of their properties against developers seeking to profit from the high demand.Mayors have been caught in the middle, aiming to accommodate an influx of new residents who help boost the local economy without displacing those who have lived in their cities for decades. They have also faced intense pressure from influential developers and business groups that have pressed for the ability to develop new homes, as well as from landlords who enjoy high rents and fear seeing those values diluted.The result has been a range of policy measures, including reforming zoning codes to encourage more development, creating new tools to finance affordable housing projects and rules mandating that developers include affordable units in their properties.These measures have shown some signs of reducing rents, for both the rich and, to a lesser extent, the middle class.For renters in the middle third of the income distribution, average rental prices have remained virtually unchanged since last summer, according to the Zillow data. Rents over the past year have also fallen slightly for the middle class of renters in Portland, Chicago, Philadelphia and Seattle.The lack of affordable housing can be particularly pronounced in smaller cities such as Portland, which has struggled to accommodate about 40,000 new residents since 2010.From 2010 to 2014, the city built only a few hundred affordable housing units, according to a city report. Since 2014, more than 95 percent of private construction in the city has been in "the luxury end of the market," said Nick Fish, a city commissioner.Private housing construction has exploded in Portland's downtown area, along its south waterfront and in its historically black northeast community. But even as the city's population has ballooned, its black population has decreased since 2014 by an average of 800 people every year, probably pushed out by gentrification, according to a study by Portland State University researchers.In an email, Portland Mayor Ted Wheeler (D) pointed to 948 affordable rental units expected to open in 2018 and an additional 978 units scheduled for 2019. "We are actively creating housing options at every income level in every area of the city," he said, adding that 10,000 more units are coming soon. "Our efforts are beginning to pay off: This will be the largest number of affordable units ever produced by the City of Portland in a single year in modern history."But for Rakhelya Levitskaya, a 66-year-old home-care aide who works with the elderly and disabled, little help appears to be on the way. A Ukrainian immigrant who has lived in the same Portland housing complex for 18 years, Levitskaya received notice of an approximately 10 percent rent increase this summer that she fears will push her into homelessness."I'm afraid of living out on the streets, without a house," she said in an interview. "I'm very worried."