However, as Hillary Clinton’s experiences with her private email server and the 2012 attack in Benghazi show, prolonged investigations take a toll. And within the Sanders ranks, there is some talk of conspiracy.

RoseAnn Demoro, executive director of National Nurses United and a leading Sanders supporter, said she believed some in both parties were hoping the investigation would hurt Mr. Sanders because he is challenging the entire political establishment. “Bernie is the only person out there with a populist base who could actually win the presidency right now, and they are trying to take him out,” Ms. Demoro said.

Not everyone is so enamored with Mr. Sanders’s continuing power. Stu Loeser, who owns a media strategy firm and was a longtime spokesman for Mayor Michael R. Bloomberg of New York, said Mr. Sanders had missed his “once in a lifetime chance” to be president.

“His people are worried that his best days may be behind him,” Mr. Loeser said, “and they may be right. But that’s not going to be because of a paperwork snafu regarding his wife.”

A federal law enforcement official, who declined to be identified because the matter was still under investigation, confirmed that the authorities have been looking into the land deal.

To finance the land purchase, the college borrowed from a bank and obtained additional financing from the diocese, according to David V. Dunn, a Burlington College trustee at the time. The college needed to demonstrate that it had the financial resources to pay the bank loan, which it did with Ms. Sanders’s assurances that it would receive $2.6 million in donations and increase its enrollment, Mr. Dunn said.