The Pope's decision not to accept the resignations will now intensify protests during his visit to the UK next month.
Auxiliary bishops Eamonn Walsh and Ray Field submitted their offers of resignation eight months ago after being named in the Murphy Report into cover-ups of paedophile clerics.
Pope Benedict's decision unleashed a furious reaction from victims of child clerical abuse here and the US, with predictions that protests by abuse groups will be stepped up as a result when he visits Scotland, England and Wales.
The decision was being interpreted as a rebuff to the authority of Archbishop Diarmuid Martin, who called for all named in the Murphy Report to account for their actions.
Bishops Walsh and Field will remain as auxiliary bishops and are to be assigned revised responsibilities within the diocese, including confirmations.
The two bishops had been continuing in their normal duties pending the decision.
Two other bishops named in the Murphy Report, Bishop Donal Murray and Bishop Jim Moriarty, have had offers of resignation accepted.
A fifth bishop named in the report, Bishop Martin Drennan of Galway, has resisted calls for his resignation.
Last spring, the Archbishop of Armagh, Cardinal Sean Brady, decided not to resign despite his involvement in an investigation 35 years ago of a case involving paedophile priest Brendan Smyth.
Astonished
Clerical abuse survivor Andrew Madden said he was not surprised to hear the resignations had not been accepted.
"Since the Murphy Report was published the Catholic Church in Ireland and at Vatican level has failed to take responsibility for the findings of that Report, in particular, the finding that sexual abuse of children by priests was covered up by Archbishops and Bishops for decades," he said.
John Kelly co-ordinator of the support group Survivors of Child Abuse (SOCA) said he was "astonished" by the news.
The US based group SNAP (Survivors Network of those Abused by Priests) said the Pope was "rubbing more salt into the already deep and still fresh wounds of thousands of child sex abuse victims and millions of betrayed Catholics."
The Pope had done "irreparable damage" to the already deeply damaged image of a selfish church hierarchy, it said.
Abuse survivor Marie Collins said she was at a loss and "past being angry" at the decision.
There was no hope the the Pope was going to change anything. She felt survivors were entitled to an explanation why Bishop Moriarty's resignation was accepted but Bishop Walsh and Bishop Field's were not.
Deirdre Kenny, of One in Four described the Pope's decision as "extraordinary."
Ellen O'Malley-Dunlop of the Dublin Rape Crisis Centre also questioned the decision.
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