Victims of clerical child abuse have strongly criticised the decision by Pope Benedict XVI not to accept the resignations of Bishops Eamonn Walsh and Raymond Field.
The two auxiliary bishops had offered to step down on Christmas Eve 2009, in the wake of the Murphy Report into clerical child abuse in the Dublin Diocese.
Both men will now be assigned revised responsibilities.
Andrew Madden, clerical abuse victim and campaigner, said the two bishops should be allowed to step down.
Dr Walsh has been a bishop for 20 years and ran the diocese of Ferns for four years after Brendan Comiskey resigned as a bishop over his cover-ups of abuse.
Dr Field has served for 12 years in Dublin.
Both bishops initially resisted calls for their resignation.