Heather Perrin's defence tried to have a media blackout imposed on her trial last year.
They argued that coverage would prejudice Perrin's second trial, which was due to begin in March but which has now been cancelled.
At the start of her trial last November, Judge Mary Ellen Ring agreed it could be reported after hearing counter-arguments from lawyers from several media organisations.
She agreed to allow reporting on condition that no mention was made of the second trial or of the defence application.
Before the trial, the defence made an application to prevent reporting. The prosecution supported the application, but did not concede that publicity would endanger the second trial.
Defence counsel Patrick Gageby said the case would attract a large amount of publicity, which would impact Perrin's right to a fair trial in March.
He said the alternative was to defer her second trial, but this could lead to "the media dictating the order of the court".
Judge Ring adjourned the matter to allow media representatives to respond.
The Irish Independent said forbidding reporting of the trial would create a precedent that would have "far-reaching consequences".
The 'Irish Times' said the press were the "eyes and ears of the public" and the Supreme Court had previously protected their right to report trials.
Judge Ring rejected the application, but told counsel they could raise the matter again if they felt any reportage was unfair.