By then, Mr. Litton was a veteran of the Hostage Rescue Team and multiple deployments to Iraq, and his wife was a counterintelligence agent in the bureau’s Washington field office. They were charged with making false statements, and both were suspended without pay. They had to halt the in vitro fertilization treatment they had scheduled for the following month. Instead, the $50,000 they had saved was used to pay lawyers.

The same month as Mr. Litton’s arrest, the F.B.I. completed his performance review. He received an excellent rating, and his superiors wrote that he had represented the F.B.I. and the rescue team in an “exemplary manner” and “maintains high standards of professionalism.”

Neither of the Littons worked for more than 500 days while they were suspended without pay. Eventually, the criminal case against them fell apart, and prosecutors dropped the charges in November 2010 and later declined to refile them.

They returned to work in February 2012, but their ordeal was not over. The Justice Department’s inspector general was continuing a separate inquiry, and in February 2014, the F.B.I. notified both of the Littons that the government intended to fire them.

They had, the F.B.I. said, provided false or misleading information on the medical forms and exhibited a lack of candor during the internal inquiry. Investigators also concluded that fertility problems were not the only reason Mr. Litton had started taking the drugs. Emails indicated that he might have been using them to improve his performance on the rescue team, which Mr. Litton denies.

They were again suspended without pay. And that September, the couple were finally fired.

The decision infuriated Mr. Litton’s lawyer, Kristin D. Alden, whose firm specializes in representing federal employees. “Medical records show he was dealing with infertility issues as far back as 2001,” she said. “We gave it to the F.B.I. before he was fired. It didn’t matter.”