“My kids don’t stop getting sick,” she said in Spanish.

She has been waiting for Nycha to send someone to fix her living room heater since last December, according to work orders reviewed by The Times. She submitted three heat-related work orders this year, but workers showed up only once and then left without fixing the heater, she said.

On a recent evening, Mr. Badia wrapped a purple blanket around his feet and lounged on a red couch in his living room. Heat radiated from the $90 electric space heater he had purchased.

“Imagine, I work in the cold all day and then I come home to the same cold,” said Mr. Badia, 44, who works delivering pizza late nights into the early morning.

Ms. Badia has reported the lack of heat to Nycha six times since Oct. 26 through a mobile app residents use to request repairs, according to records reviewed by The Times. Nycha closed five of the work orders within 24 hours without having anyone show up, Ms. Badia said.

Robin Levine, a spokeswoman for Nycha, wrote in an email last week that on one occasion a resident in Ms Badia’s apartment did not allow workers to enter the apartment, a claim Ms. Badia disputed. Ms. Levine did not elaborate on the circumstances behind the other closed work orders.

Ms. Levine said, in general, heat in the apartments was escaping through windows and doors in need of additional insulation. She said the heaters were working and recommended that residents move furniture away from the heater to increase heat circulation.

But during a recent visit by a reporter, only a small trickle of tepid air emanated from the heaters in several apartments. Ms. Badia said her daughters were sleeping with an electric space heater at night because of the cold.

“How am I going to tell my children to not turn them on?” Ms. Badia said. “If I have to spend all of my income in electricity, I’ll do it. I’m not going to let my children suffer.”