Clerical errors are common, said Mr. Clark, whose store opened in 1960 and was inspected by the A.T.F. this year. As long as dealers work with the A.T.F. to correct errors and file correctly, the violation is rarely seen as serious.

“Some gun shops consider it a pain. They feel like the A.T.F. is the bad guys,” Mr. Clark said. “The whole idea here is to catch bad guys. I want bad guys to not have guns just as much as anybody.”

“Most gun dealers abide by the law and are really careful to sell guns in a responsible manner,” said Avery Gardiner, the co-president of the Brady campaign. “There’s a small number of gun dealers engaged in really irresponsible practices, putting everybody at risk, and the A.T.F. knows exactly who they are and allows them to continue operating.”

For gun dealers to lose their licenses, the A.T.F. must prove they “willfully” violated the Gun Control Act. Violating the law is not enough to justify the loss of a license; inspectors must prove that store owners knew they were acting illegally.

“Other regulatory statutes don’t have that,” said Adam Winkler, an expert on constitutional law and gun policy. “This is part of a larger pattern in the federal gun laws that make it hard for A.T.F. to enforce.”

In the bureau, one former A.T.F. inspector said, that standard was seen as difficult to uphold in court, where dealers would almost certainly appeal the A.T.F.’s decision. That prompted supervisors to overrule inspectors’ recommendations to revoke licenses, said the former inspector, who requested anonymity because he continues to work with the gun industry.

To prove violations were willful, the A.T.F. seeks to establish a record of warnings. In warning letters, senior A.T.F. officials told dealers that violating the Gun Control Act again could jeopardize their license. But a review of A.T.F. records showed that even when stores had received such warnings and continued to violate the law, supervisors let them keep operating.