In late September, a woman in her 70s arrived at a skilled nursing facility in suburban Houston after several weeks in the hospital. Her leg had been amputated after a long-ago knee replacement became infected; she also suffered from diabetes, depression, anxiety and general muscular weakness.

An occupational therapist named Susan Nielson began working with her an hour a day, five days a week. Gradually, the patient became more mobile. With assistance and encouragement, she could transfer from her bed to a wheelchair, get herself to the bathroom for personal grooming and lift light weights to build her endurance.

That progress ended abruptly on Oct. 1, when Medicare changed its payment system for physical, occupational and speech therapy in nursing homes. Ms. Nielson, employed by Reliant Rehabilitation, which supplies therapists to almost 900 nursing facilities, said that her allotted time with the woman was reduced from 60 minutes to just 20 or so minutes a day, not even long enough to help her leave her bed.

“I’m not able to do my job,” Ms. Nielson said. “This person had the potential to do more, and I couldn’t help her.”