The group, believed to be the first all-amputee team to undertake the challenge, set off from the Canary Islands on 20 December.
Two of the rowers have reportedly struggled to eat anything since they set off, a spokeswoman said.
They have also been sent "flying off their seats", by heavy sea swells.
Lee Spencer, Nigel Rogoff, Paddy Gallagher and Cayle Royce, aged 29 to 56, were among 26 crews which set off from La Gomera to Antigua in the Caribbean.
Cayle Royce - 29, from Dartmouth. Suffered serious injuries serving in Afghanistan
Paddy Gallagher - 30, from Cambridgeshire. He was injured in Afghanistan while serving with the Irish Guards
Nigel Rogoff - 56, from Hereford, who lost his leg while taking part in an RAF parachuting display
Lee Spencer - 46, from Yelverton in Devon. He lost a leg when he was struck by debris when he stopped to rescue a seriously injured motorist on the M3
Mr Spencer, who spoke to his wife, Claire, on BBC Radio Devon, wished his family a Merry Christmas and said he was "really looking forward" to seeing them at the finish in Antigua.
Mrs Spencer told him he was "mad", but she was "very, very proud" and she would "raise a glass, or five, [to him] in the pub".
They aim to row the 3,000 miles in under 55 days, but with another 2,453 miles to go, the team has reported on Facebook that "sea sickness has well and truly kicked in with two members of the team struggling to eat anything since they set off".
They also report that the strong north-easterly winds have have also brought a "new challenge" with a battle between the swell and the oars.
A spokeswoman said: "The seas are quite rough and the oars keep pushing into their prosthetics.
"The big swell is also putting them off course so they are hoping for calmer conditions to get back on track."
The Talisker Challenge is branded as "the world's toughest row".
The spokeswoman said: "The first two weeks are known as hell on earth and it takes that long to adjust before they get in their stride.
"It's a long journey ahead. This is day four and there are at least another 45 days ahead."
The crew members come from Devon, Hereford and Cambridgeshire.
Four ex-serviceman attempting to row across the Atlantic have been hit by severe sickness since setting off.