At first, it was one doctor quitting the tiny Ukiah Veterans Affairs Outpatient Clinic in Northern California. Then another left, and another, until of the five doctors there a year ago, only one remained.

The Veterans Choice Act, passed by Congress amid scandalous stories of hidden waiting lists at Veterans Affairs hospitals, allowed more veterans to get care from private providers, but it created an avalanche of paper at Veterans Affairs facilities as outside doctors sent in information on patients. Veterans Affairs doctors had to enter so many medical records manually into the aging department health records system that it crippled their ability to see patients.

“I was working nights and weekends, holidays, and I couldn’t keep up,” said Dr. Neal Elkin, a primary care physician who left the Ukiah clinic in January. “I was so stressed, I couldn’t sleep. My asthma started getting bad, and I just burned out.”

In Washington, the leadership of the department had been working to streamline private care and overhaul its computer system to cut paperwork. Then President Trump plunged the department into turmoil. He fired the Veterans Affairs secretary, Dr. David J. Shulkin, by tweet in March after weeks of infighting. His handpicked replacement, Dr. Ronny L. Jackson, saw his nomination collapse last week amid a barrage of accusations related to his work as the White House physician. Meanwhile, a string of departures at the highest level of the agency has left it adrift.