A maintenance worker showed up to take a look, and repairs were scheduled.

A plasterer would come to fix the hole in May 2011. A painter would come to cover up the plasterer’s work in May 2012.

The drip has yet to be fixed.

The situation is no better in Newark, which has shuttered 600 units that it cannot afford to fix. The city was given federal approval to raze 1,004 more, but it cannot pay for the demolition.

In Washington, the District of Columbia Housing Authority has floated bonds, among other measures, to put $140 million into fixing up its developments, but it is still $200 million short of what the authority says it needs for repairs.

Baltimore’s housing authority needs $860 million for crucial repairs, said the housing commissioner, Paul T. Graziano; it has demolished or shuttered 33 percent of its units since the 1990s and has another 600 “on the verge of failure,” with falling cabinets, unhinged doors and aging electrical systems.

All told, the country’s housing authorities still need $22 billion to $32 billion to rehabilitate their buildings, said David Lipsetz, a senior adviser in the Office of Public and Indian Housing with the Department of Housing and Urban Development  an average of $25,000 for each of the 1.175 million public housing units. But that figure is based on a 1998 study, he said; an updated report is in the works.