The family of Nancy Guthrie issued a new appeal on Saturday for information on the whereabouts of their missing grandmother, six months after she disappeared from her home in Tucson, Arizona, and a day after local investigators released two purported ransom notes.

“Six months ago, someone took her out of her bed in the dead of night. We have lived every moment, every breath, and every heartbeat in agony and despair ever since,” a post on Instagram said.

“Every day, we wake up and try to be strong and go on – because that’s what our joyful and resilient Mom taught us to do. But make no mistake – our hearts are in ruins,” the Guthrie family added.

Eighty-four-year-old Nancy Guthrie, mother of Today show anchor Savannah Guthrie, disappeared from her home on 1 February. But despite intense national attention and the involvement of the FBI, no suspects have been arrested in connection with her disappearance.

On Thursday, NBC News reported that two men who were detained and questioned in the days immediately after Nancy Guthrie vanished had issued a “notice of claim” against the Pima county sheriff, Chris Nanos, and a detective on the case.

The Pima county sheriff’s department posted a message saying, “The Guthrie investigation remains active and ongoing,” and later released notes received by news outlets soon after Guthrie disappeared.

The first note came from someone who claimed they had Guthrie – and that “she is safe but scared” and would not be released until payment in the form of $4m in bitcoin was received.

The second said that she had “perished shortly after she was taken. We believe it was heart related. She is buried in nature now.” The presumed abductors added: “Nothing you could have done could have changed the outcome. We want your family to know this and hope you all can find peace. We are truly sorry.”

On Saturday, the family issued a new appeal for information leading to Guthrie’s recovery.

“We are begging for help. We are desperate. We need someone to come forward. Someone knows something. Someone suspects something. Someone recognizes the writing in the ransom demand notes,” it read.

“Please. Bring her home,” the appeal concluded.