WASHINGTON — Facing a well-financed insurgency in Afghanistan, the United States has struggled for years to cut off the main contribution American taxpayers make to Taliban coffers: the hiring of Afghan contractors with ties to the insurgents.

But despite the development of contractor blacklists and other requirements earlier in the war, American investigators have uncovered a new case that casts doubt on the military’s ability to weed out suspicious contractors from the thousands who work with the United States to build bases, ship supplies and carry out myriad other tasks.

The case centers on the Zurmat Material Testing Laboratory, part of the Zurmat Group, an Afghan company that the investigators say was paid to do work at an American-controlled facility in November 2012, despite having been blacklisted two months before by one part of the military for providing bomb-making materials to insurgents.

The Zurmat case was outlined in a letter sent last week to Defense Secretary Chuck Hagel by the Special Inspector General for Afghanistan Reconstruction, an internal government watchdog. A copy of the letter was provided to The New York Times.