Sgt. Mark Salesse, 44, was training with others when an avalanche swept him off the Polar Circus ice-climbing route in Banff National Park last week.
His mother, Liz Quinn, and her husband, Robert Brady, issued a statement Tuesday saying military officials had updated them on the recovery mission.
They said they've been told that their son is beneath at least 4 1/2 metres of snow.
In an interview with The Canadian Press, Quinn said the loss is a harsh reality and hard to accept.
"It didn't come as a surprise, but it was something I was really trying not to hear. I didn't want to hear it," she said from home in Moncton, N.B.
"I really, really had hoped from the bottom of my heart that if anybody was going to survive this it was going to be Mark," she said.
"When I am faced with the facts...you know that there's no way anyone would have made it."
Quinn said her son joined the military when he was 18 and turned down a mission to Afghanistan when the search-and-rescue opportunity came along.
She described the six-foot-five-inch Salesse as a "machine" of a man, who was physically active and enjoyed competition.
"He was a tall, strapping lad but he was a very gentle soul.
"He was a very giving person. He was selfless."
Quinn said Salesse survived a fall during training in Colorado in 2011 and shattered his pelvis. He wasn't expected to walk again but he managed to get himself back in shape.
Crews were still trying to reach Salesse after having to call off a short search on Monday due to the threat of further avalanches.
His parents said that if his body is not found in the next week, the search will resume in the spring.
"They will continue searching for Mark and bring our beautiful loving son home to us," they said.
"Mark has died doing what he loved most, in the majestic mountains that so beckoned him. He chose his final resting place. He is at peace."
Parks Canada has said that additional avalanches — both natural and ones triggered to improve safety — have fallen on the area where he is believed to have been buried last Thursday.
Salesse, who was based at CFB Winnipeg, was swept off a narrow ledge when weather conditions changed quickly during a military exercise.
A spokesman for Parks Canada has said Salesse wasn't wearing an avalanche transceiver, a device that allows rescuers to hone in on a signal and locate buried victims. Searchers are using dogs to try to pick up his scent.
Quinn said she agreed to talk to the media because she wants her son to be remembered.
"I don't want Mark to be just a casualty. I want him to have a name and a face, because he worked very hard for the Canadian people for the last three decades."
— By Bill Graveland in Calgary
Follow @BillGraveland on Twitter
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