Two paramedics had trekked about 40 minutes to the base of the glacier in the upper reaches of the Rakaia River, west of Christchurch, where the woman lay unconscious in a tent.
The paramedics had stabilised her broken limbs before packing her into a survival bag in preparation for the trip back across the ice. As they did they heard the thunder of an avalanche that had crashed down frighteningly close to them.
They had managed to get her to the chopper and taken her to Christchurch Hospital.
Ms Rhodes has been unconscious since the accident. Her mum, Ann Rhodes, of Greytown in Wairarapa, as well as brother Colin and two sisters Marion and Janet rushed to her bedside in the intensive care unit.
Speaking from the family home in Greytown yesterday, father John Rhodes said Heather was in a stable condition, but had shown "minimal improvement".
"She's not been conscious since the fall and that, of course, is the critical thing as far as we're concerned," said Mr Rhodes, himself a keen tramper who has scaled several mountains with his daughter.
"While it's giving her body a chance to mend, it has not been possible yet to assess the extent of her head injury."
Mr Rhodes said Heather had "lived in the outdoors" her whole life.
Since graduating from the University of Otago, she had worked on the Outward Bound course, the Sir Edmund Hillary Outdoor Pursuits Centre of New Zealand, and most recently as an instructor in the army leadership centre based at Burnham Military Camp.
In 2011 she had scaled Aoraki-Mt Cook almost a century to the day after the first woman conquered New Zealand's tallest peak. Ms Rhodes, who lives in Christchurch, left the Burnham job in June and her dad said she had been planning her next employment move. News that she had been involved in an accident had come through a series of "garbled" phone messages on her parents' phone picked up on Monday. Mr Rhodes said after piecing together what had happened the family had scrambled to be by her bedside.
A Westpac rescue helicopter paramedic praised the actions of Ms Rhodes' climbing companions who had had all the right gear and
Mr Rhodes was full of praise for the climbing companions and the rescuers. "They did phenomenally well," he said.
"I'm an outdoors person and a tramper, but not at all skilled on the rescue side of things. But everything I've heard is that they did everything right in an incredibly difficult situation.
"And the Westpac rescue helicopter team - the pilot and paramedics - are very, very good at what they do, and we're just so grateful to them too."
Mr Rhodes has remained at home in Greytown, "holding the fort, fielding calls and hundreds of emails".
Through her outdoors work Ms Rhodes had built up an "incredibly large" network of friends, he said. "I've got emails coming in from all over the world from worried people wanting to know what's going on," he said. "We're all just waiting for some good news."
