The jury has been discharged and the case will now be relisted for another hearing before a new jury unless a settlement is reached in the meantime.
John McCauley, aged 46, a property consultant originally from Donegal but now based in Dubai and Lithuania, had sued over an article in which Ms Power criticised him for taking a midwife to court over the interruption of him filming the birth of his first child.
After a second day of deliberations, the jury said it was unable to reach a unanimous or majority verdict in relation to one of two questions they were asked. It had reached a verdict on a question of whether the words used in the article were true or false insofar as they allege facts.
However, it was unable to reach either a unanimous or majority verdict in relation to a second question over whether the words constituted honest comment on a matter of public interest.
The foreman told Mr Justice Eamon de Valera the jurors felt they would not reach a majority decision.
Mr Justice de Valera said in those circumstances he would discharge the jury, which comprised of seven women and four men, as one juror was excused last Friday due to a prior holiday commitment.
The judge, who said it was the longest time a jury had been out in his experience, thanked them and excused them from jury service for 10 years.
The case, which lasted five days, centred on a Mar 2009 article written following publicity surrounding another case brought by Mr McCauley against midwife Iris Halbach and Mount Carmel Hospital in Dublin. Mr McCauley claimed Ms Halbach had acted unreasonably when she asked him to stop filming momentarily after the birth of his child as she worked to clear his baby’s airways in 2006. That case was dismissed in the circuit court.