The Hawke's Bay woman desperately wants to visit the place where her father died but has missed out on a seat.
Her sister Raylene was chosen by ballot to go under her father's name and her mother was chosen as a family representative for Brehaut.
"There are not many of us left who want to go but they say this is the last flight - no more," Mildenhall said.
"They have cut themselves short of doing the full job by leaving behind the few of us who desperately want to go."
She had not heard from Air New Zealand and knew nothing about the flight this month.
"Yet again we find out through the media - just like we did 35 years ago. Not much has changed."
Mildenhall had considered a boat trip to the ice but could not afford the $30,000 cost.
The first Air New Zealand trip was in late 2009 to commemorate the 30th anniversary of the disaster, New Zealand's worst aviation accident.
An Air New Zealand representative confirmed the third flight would be made this month.
"Family representatives will travel to Antarctica completing the last of a series of private family memorial visits to the ice."
The flight will be operated on an A319 charter aircraft. Once on the ice, family members will take part in a private commemoration ceremony.
Six family members travelled to Antarctica in 2009 and 104 travelled on the second flight in 2012.
All 237 passengers and 20 flight staff on board Air New Zealand Flight 901 died in the crash.
The death toll included 180 New Zealanders, 24 Japanese and 22 Americans.
