“Before, I could just drop by five days a week,” said the Rev. Justin Van Orman, a Lutheran pastor who moved back to Mobridge to be closer to his 79-year-old father, Robert. “He knew I was there.”

Not long after Mr. Van Orman’s father moved from Mobridge to a new nursing home about 50 miles away, Mr. Van Orman got a call saying his father had fallen out of bed. Mr. Van Orman had to decide: Should he upend his day to check on him, or wait and take the nursing home’s word that his father was O.K.?

Similar scenes are playing out in other heavily rural states. Five nursing homes closed in Nebraska last year, with more at risk of closing. Six shut down in Maine — a record, according to the Bangor Daily News.

Thirty-six rural nursing homes across the country have been forced to close in the last decade because they failed to meet health and safety standards. But far more have collapsed for financial reasons, including changing health care policies that now encourage people to choose independent and assisted living or stay in their own homes with help from caregivers.

Some nursing homes cannot find people to do the low-paying work of caring for frail residents. Others are losing money as their occupancy rates fall and more of their patients’ long-term care is covered by Medicaid, which in many states does not pay enough to keep the lights on.

South Dakota chips in less than any other state in the nation to pay for long-term care for residents on Medicaid, said Mark B. Deak, executive director of the South Dakota Health Care Association. He added that the state’s low payment level — a product of South Dakota’s fiscal conservatism and distrust of government-run health care — has now created a crisis.