Many of the levees, usually earthen and topped with grass, were built by farmers decades ago and are now managed by a patchwork of local government agencies known as levee districts that often do not coordinate or even follow the same rules. With increased flooding in the past few years, the levees are being tested more frequently than ever before, straining the finances and expertise of some of those districts.

The levee situation has become so grave that the American Society of Civil Engineers gave the country’s levee system a D grade in 2017, suggesting $80 billion in investment over 10 years.

“When the next one comes along bigger, they either fail or are overtopped again,” said Nicholas Pinter, an expert on rivers and flooding at the University of California, Davis.

According to the United States Army Corps of Engineers, which oversees infrastructure on the Missouri River and some of its tributaries, at least 62 levees had been breached or overtopped in the Midwest in March, and hundreds of miles of levees had sustained damage.

“When they run water over the top of them, there’s not anything you can do,” said Pat Sheldon, the president of a rural levee district in southwest Iowa that was still paying off repairs from the 2011 flood. This time, Mr. Sheldon said, the damage to the levees was much worse, perhaps in the hundreds of millions of dollars. “It’s terrible,” said Mr. Sheldon, whose farm was also cut off by the water.

In Missouri, Mr. Bullock pointed out a levee that last week had been split open and consumed by the river. A large log swirled in the water near where the earthen berm should have been. “I don’t know what we’re going to do this time,” he said.

The Army Corps of Engineers, which helps determine water levels by operating a series of dams on the Missouri River, tries to balance the needs of many who use the rivers it manages, including farmers, barge shippers, endangered animal species and people who use the water for recreation. Those interests are sometimes at odds, and have been the subject of decades of litigation. Corps officials say they are not allowed to change the congressionally authorized purposes of the reservoirs, though they had been most focused on limiting floods for the past year.