But the case won’t go away. Last week, The Irish Examiner and the public broadcaster RTE’s “Prime Time” program reported that Ireland’s child protection agency had created a file on Sergeant McCabe containing a false accusation of child sexual abuse — a mistake that the agency has attributed to what it called a clerical error. The news organizations also reported that this wasn’t the first time Sergeant McCabe had been wrongly accused of such a crime; an earlier complaint against him had been made, in 2006, and dismissed.

The disclosure that a whistle-blower could face such accusations in apparent retaliation has raised unsettling questions about Ireland’s culture of policing and the possible collusion of other agencies, including the child protection agency.

The case has affected the highest levels of the Irish government, bedeviling Mr. Kenny. He has been attacked by critics who charge that he missed opportunities to resolve the mess in 2014, and supported the police chief at the time and his justice minister for too long.

Mr. Kenny failed at first to give a complete account of when he learned of the false abuse allegations, and has insisted that he knew nothing of a broader smear campaign — an assertion that his critics in Parliament have contested.

There were heated exchanges between Mr. Kenny and Gerry Adams, the leader of the opposition Sinn Fein party. At one point, Mr. Kenny called Mr. Adams an “absolute hypocrite” and attacked him for playing down, years earlier, the case of a former Sinn Fein member who said she was sexually abused by IRA members — a charge that Mr. Adams denies.