The New Zealand Government and its coalition allies have been searching for Ms Akavi since she was kidnapped by armed gunmen in Syria more than five years ago.
A senior government source said they had not given up hope she was still alive, but with a complete absence of any new information or positive sightings in recent months, that hope is now dwindling.
Over the years there have been various sightings of Ms Akavi and reports she was alive, including that she provided medical care in an 'internally displaced persons camp' in Iraq in late 2017.
The last 'concrete' sighting received by intelligence officials was that she had been seen late last year in different places close to the Syrian Iraq border.
There were hopes she would be found either when the IS stronghold of Baghouz was overrun, or picked up among the people trying to flee the area.
The International Committee of the Red Cross broke its silence in April this year, calling for information that could help locate Ms Akavi and the two drivers captured alongside her.
In April Foreign Minister Winston Peters said the Ministry of Foreign Affairs and Trade had led a "significant and sustained whole-of-government effort ... involving a wide range of other agencies, and cooperation with international partners".
That included the deployment of a "small multi-agency team" based in Iraq, which was "specifically focused on locating Louisa and identifying opportunities to recover her".
The Government is making no comment about the current status of that team, which included special forces troops from the New Zealand Defence Force.
Kayla Mueller and the US military raid
Ms Akavi was held captive alongside Kayla Mueller, an aid worker from the United States, for what's thought to be at least four-and-a-half months.
The US military operation over the weekend against Abu Bakr al-Baghdadi was named after Ms Mueller, in her honour.
Ms Mueller is said to have been killed in February 2015; her mother Marsha told RNZ in April that Ms Akavi had helped her daughter - and she hoped she would still be found alive.
"Kayla spent a lot of time in isolation while she was there - she was captured in August of 2013, you know, Louisa and her colleagues were captured in October.
"Kayla was with other women that we do know of, but for shorter periods of time and the information we got from them on how strong Kayla was, and how together they were able to cope so much better is amazing."
One possible theory had been that Ms Akavi was kept close to Abu Bakr al-Baghdadi because of her nursing background, and his death raised hopes some information may have been unearthed after the raid.
However, the government source said there was no evidence so far that she had been with him, or in the vicinity, but the Government was still seeking any further information that may be relevant to her.
Comments
The PM should keep in contact with trump like australia does//// trump and the us military have done great work / with little interest from our government/
it should be of high interest the missing nurse ///