A nursing shortage — driven by the pandemic — has made life miserable for parents with profoundly disabled children. “What if I’m so exhausted that I make a mistake?”

It was 9 a.m. on a Sunday in May, and Chloe Mead was already worn out.

In her living room, she cradled her 7-year-old son, Henry, supporting his head with one hand and helping him toss a ball with the other, careful not to disturb the ventilator that was keeping him alive. A nearby monitor tracked his blood-oxygen levels and a pump was at the ready should his tracheotomy tube need cleaning. In the corner, her 4-year-old daughter was building a pillow fort.

“I need, like, five extra arms,” she said.

Ordinarily, she wouldn’t be by herself. Since infancy, Henry, who has spinal muscular atrophy, a rare muscle-wasting disorder, has had intensive, round-the-clock nursing at home, with Ms. Mead and her husband serving as fallbacks when a nurse unexpectedly cancels a shift.

But the recent shortage of home-care nurses has forced the couple, who live in Queens, to handle longer and longer periods on their own — as many as 36 hours at a stretch. That morning, her husband, Andy Maskin, was catching up on sleep so he could take that night’s late shift, from 2 a.m. until 7 a.m., when he begins his own workweek.