The Chief Justice has "very reluctantly" agreed to postpone a meeting with Mr Justice Seamus Woulfe for the third time.
They were due to meet today to discuss the fallout from the 'Golfgate' controversy.
The Supreme Court judge attended the Clifden dinner event in August which breached COVID-19 restrictions.
Today's scheduled meeting was the third attempt by the two judges to convene after it was postponed on two occasions last week, the latter at the request of Mr Justice Woulfe for medical reasons.
A spokesman for the Chief Justice Frank Clarke said this afternoon that Mr Justice Woulfe had requested a further delay of the meeting.
Today's meeting was due to take place between the Chief Justice and a colleague of the Supreme Court with Mr Justice Woulfe and a judicial colleague of his choice.
At the request of Mr Justice Woulfe’s colleague, the Chief Justice and Mr Justice O'Donnell met with that colleague.
Mr Justice Woulfe made the request for the postponement through his colleague.
The Chief Justice said that, as a result of what was said, he is "very reluctantly" willing to make "one final postponement" until Thursday.
However, he indicated his "very serious concern as to the damage which the continuation of this process is causing".
The statement added: "The Chief Justice has made it clear that, should the meeting not go ahead as scheduled on Thursday, he will make alternative arrangements to convey his final views on the process to Mr Justice Woulfe.”
81 people attended the highly controversial golf dinner event at a hotel in Clifden last August.
The 'Golfgate' scandal led to the resignation of attendees like Agriculture Minister Dara Calleary and Ireland's EU Commissioner Phil Hogan.
Senator Jerry Buttimer also resigned as Leas-Cathaoirleach of the Seanad.
A subsequent review of Mr Justice Woulfe's attendance by former Chief Justice Susan Denham found he should not be forced to resign over the scandal.
She said this would be unjust and disproportionate.
