Former Defence Forces member Lisa Smith must be charged with a criminal offence or released from Garda custody without charge by about 10.30am on Wednesday.
She was questioned by gardaí as part of a criminal investigation into suspected terrorist offences abroad.
She was taking a cooperative approach in questioning; responding to questions but effectively claiming she travelled to the so-called Islamic State for religious reasons rather than any terrorist activity.
Gardaí have seized a number of devices, including mobile phones and laptops, in a bid to determine who she was in touch with in Ireland and other jurisdictions while she was in Syria and Turkey.
Detectives have also sought the assistance of international intelligence agencies in a bid to determine if the information on Islamic State and foreign fighters gathered by those countries may relate to Ms Smith.
The Co Louth woman (38) appeared at the Criminal Courts of Justice in Dublin on Tuesday morning for a brief hearing to approve a Garda request that her detention be extended for a third 24-hour period.
Ms Smith has been questioned at Kevin Street Garda station following her arrest on Sunday after her return to Ireland on a Turkish Airlines flight from Istanbul along with her daughter (2). Her period of detention had already been extended by 24 hours on Monday.
On Tuesday, Judge Patricia McNamara agreed to the extension following a hearing at 9.25am, an hour before the previous extension was due to expire.
Ms Smith, who sat in the court accompanied by a garda, was represented by solicitor Peter Corrigan of Belfast-based law firm Phoenix Law.
Dressed in black, she left court with her head covered with a coat and scarf. She was walked by a female detective to an unmarked Garda van to bring her back to the station. She remained in Garda custody late on Tuesday night and was being questioned under Section 30 of the Offences Against the State Act.
Darragh Mackin of Phoenix Law, speaking on Monday, said "no evidence of any kind" linking her to a terrorist offence had been put to Ms Smith in questioning. His client had a "strong case" to make in arguing that she was a member of Islamic State but not directly involved in terror organisation Isis, he said.