His sixth child has spent time on a ventilator in intensive care at Alder Hey Children's Hospital in Liverpool since she was born on Sunday.
Having briefly come out of the ICU, yesterday Fury asked fans to continue their prayers as he revealed his newborn daughter was back in intensive care.
And he has confirmed that although she is now off the ventilator, she remains in ICU.
He said she yesterday had "a stable day off the ventilator" and also thanked all the doctors and nurses for their care.
Fury's wife Paris also posted on social media saying Athena was "more awake and sucking her dummy".
Today, Thursday, Fury shared with fans a photo of a birthday card from Athena to mark his 33rd birthday, which is decorated with her four-day-old footprints.
Fury announced the arrival of his sixth child with his wife Paris on Sunday.The boxer has now set up a fundraising page to support Ronald McDonald House at Alder Hey Children's Hospital, and almost £35,000 has already been raised.
Fury is donating two signed WBC belts as part of the fundraiser, which he will personally sign and hand over to the winners.
You can go online to donate and be in with a chance of winning here.
Fury has thanked everyone for their pledges, saying: "Massive thanks to everyone who has helped, u are amazing".
The couple announced that Paris was pregnant in February, and revealed they were expecting a daughter.
They have been married since 2009 and are already parents to daughters Venezuela, 11, and three-year-old Valencia Amber, and sons Prince John James, eight, Prince Tyson II, four, and one-year-old Prince Adonis.