British-Australian expedition leader Tim Jarvis and mountaineer Barry Gray were stuck at Shackleton's Gap, but had assured their team that they were doing well, although cold and wet, and would continue when the weather clears.
Four other members of the expedition and film crew recreating Shackleton's journey over a mountain in South Georgia to an old whaling station at Stromness have already been evacuated due to the extreme conditions.
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"They are both experienced mountaineers and they've said they will continue with the expedition unsupported when there is a break in the weather," crew member Paul Larsen said.
The team is aiming to recreate one of the greatest ever survival tales and has already completed Shackleton's crossing of the Southern Ocean in a lifeboat from Elephant Island off the Antarctic Peninsula to rugged South Georgia.
The final leg is a two-day climb to 900 metres (2,950 feet) over the mountainous, crevassed interior of South Georgia to reach the whaling station where Shackleton and his men raised the alarm about the sinking of their ship, the Endurance.
For the journey the men have worn only the traditional gear of early last century while during the boat trip they used only the equipment, navigational instruments and food available to Shackleton.
Their team said Saturday that Jarvis and Gray had spent 12 hours "hunkered down" in a tent to ride out the storm, which has seen wind gusts of 45 knots along with driving rain, sleet and snow, freezing temperatures and zero visibility.
Two fellow crewmen had braved the conditions to restock the pair with food and other provisions, but did so wearing modern climbing gear. Those provisions would last them until Monday.
Along with Norway's Roald Amundsen, the first man to reach the South Pole in 1911, Australian explorer Douglas Mawson and Briton Robert Falcon Scott, Shackleton was among the great Antarctic explorers.
When he set off on his third trip to the region in 1914 with the ship Endurance, he planned to cross Antarctica via the South Pole.
But the vessel became trapped in 1915, and sank 10 months later as it was crushed by the advancing ice. Shackleton and his crew lived on the floating ice until April 1916, when they set off in three small boats for Elephant Island.
From there, Shackleton and five crew made the treacherous voyage to South Georgia, reaching their destination 16 days later to face the mountainous trek.
All members of the Endurance mission were eventually rescued with no fatalities.
