David Murdoch's men missed the chance to guarantee qualification for the men's curling semi-finals at Sochi 2014 on Sunday by slipping to a 7-6 defeat against Norway.
Britain went into their penultimate round-robin match in the Ice Cube Curling Center with five wins and two defeats, knowing victory over their nearest challengers would secure a medal opportunity.
It was win or bust for Norway as GB conceded a 2-0 second-end lead to play catch-up for most of the game, levelling 6-6 with the hammer in the ninth only to lose out in the final end.
That leaves their last fixture against China at 1400 local time Monday possibly crucial, with Norway - who have two games remaining against Switzerland and Denmark - still a threat.
Murdoch remained defiantly optimistic, saying: '' I fancy our chances, I really do'', after round-robin session 10 ended with Sweden guaranteeing their semi-final berth by beating Russia 8-4 and Canada also unable to miss out.
China are in second place with six wins and one defeat, followed by Canada, who have six wins and two defeats.
Even if the Canadians lose their last game - to the Chinese in the evening session - the worst they could finish is tied at 6-3 with Norway and Team GB, and they would qualify on a superior head-to-head record.
To add to a complicated scenario, Britain could fail to beat China and still get a play-off spot should Norway falter twice, although a win for Murdoch's men would guarantee a play-off spot at least.
Britain's Zoe Gillings edged through to the semis of the women's snowboard cross in Krasnaya Polyana but was denied a place in the final by a matter of inches, and had to settle for a ninth-placed finish overall.
Gillings looked to be on course for a top three spot but was pipped on the line by Italian Michela Moioli.
Gillings said: "I'm really disappointed about the photo finish and not quite making the final, but it can be pretty small margins in this sport.
"One of the officials said I'd made it but it flashed up on the screen about 15 seconds that I hadn't.
"Lindsey (Jacobellis) fell in front of me and I had to change my line a little bit and that cost me some speed and is why I got caught on the line.
"My aim coming into the competition was to ride as well as I could and stay on my feet. This is my first Olympics where I've not had an injury."
Eva Samkova of the Czech Republic clinched the gold medal as American favourite Lindsey Jacobellis, who famously blew gold in Turin in 2006 when she fell after attempting a stunt on her final jump, slid out of contention after falling when well ahead in her semi-final.
Samkova executed a clear run to ease to victory ahead of World Cup leader Dominique Maltais of Canada, with French teenager Chloe Trespeuch taking bronze.
Britain's two-man bobsleigh team Lamin Deen and John Baines were due to go in their heat at 2015 local time (1615GMT) at the Sanki Sliding Center and Nick Buckland and Penny Coomes were scheduled for their ice dance short programme at 1900 local (1500GMT).