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 on Monday (1000GMT) possibly crucial, with Norway - who have yet to play 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 through.
Canada are in second place with seven wins and two defeats, followed by China with six wins and two losses.
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.
"I'm really disappointed about the photo finish and not quite making the final, but it can be pretty small margins in this sport," said Gillings.
"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.
British pair Nick Buckland and Penny Coomes finished 11th in the short programme - the first part of the ice dance figure skating competition at the Iceberg Skating Palace - but were disappointed to have being penalised for an extended lift again, having suffered the same fate in the team event.
Buckland again failed to put his partner down within the required sub-six seconds which meant that their score of 59.33, before the free skating programme on Monday, was a point lighter than it should have been.
Buckland said. ''I've got a bit of a music where I pick her up and put her down but it was obviously over as that's why we got the deduction.
''We easily gained more points for the lift - it's a level four - than we lost in the deduction so it's not the end of the world. We train not to lose that point on that lift, so it's frustrating when you do.''
USA pairing Meryl Davis and Charlie White led the field from defending champions Tessa Virtue and Scott Moir of Canada.
In the two-man bobsleigh British pair Lamin Deen and John Baines, a late replacement for the injured Craig Pickering, were placed 23rd after the first two runs at the Sanki Sliding Center.
Deen and Baines, both making their Olympic debuts, clocked a combined time of one minute 55.35 seconds.
They will need to be in the top 20 after Monday's third run in order to qualify for a fourth run.
Deen said: "The first heat wasn't so bad. It was probably the fastest heat we have had down this track. Push time we have improved as well.
"Craig and I before the injury had done a lot of work together on timing. For John and I this is probably the seventh heat we have had together. We have still got timing work to improve on for tomorrow.
"It will be tough to get into the top 20 but this is bobsleigh, anything can happen. The top of the track is key. If you mess that up you can fall back as easily as you can gain time."
Brakeman Baines said: "We will go back, talk to the coaches, regroup and look at the videos and see where we can improve."