British sailors Chris Draper and Simon Hiscocks endured a mixed day on the Saronic Gulf but are guaranteed a medal with one race left in the 49er class.
The pair won Tuesday's first race but were ninth and then sixth and trail leaders Spain by 11 points.
Spain look favourites for gold on 60 points with Ukraine on 69 and GB still with a slim chance of victory on 71.
With the US duo on 82 points, Britain go into Thursday's final race with an unassailable lead in third place.
To win gold overall, Draper and Hiscocks would need to win on Thursday with Spain finishing 12th or lower.
But the British pair remain undecided on whether to battle for the silver or go all out in the hunt for gold.
"We were pretty upset when we came in. We are a bit disappointed but you have
got to be positive and we could still win it," said Hiscocks, who won the silver with Draper in Sydney four years ago.
"I think it is fairly unlikely but we will go out and do everything we possibly can on the last race.
"We will just concentrate on trying to sail another race and a good race and
hopefully things will take care of themselves. That's all we can really do from
"A gold medal is what we wanted though."
Draper and Hiscocks began the day in joint second with Ukraine, nine points adrift of Spain, but edged to within two after pipping Australia in race 13 as the Spaniards finished eighth, while Ukraine dropped back.
But in the day's second race, the Britons struggled as Spain finished second behind Australia, while Ukraine were fifth and edged back to within one point of Great Britain.
In race three, Britain started badly but were boosted when fourth-placed Australia were disqualified for not performing a penalty turn after being early across the line.
America won with Norway second, Ukraine third and Spain fourth. Briton were pipped to fifth on the line by Italy.
The 49er sailors compete in 16 races with the worst two results discarded.
In race six of the two-man Star class, Britons Iain Percy and Steve Mitchell finished third and stand seventh overall with five races left.
The British duo are on the same points - 29 - as Switzerland and are just three points away from the United States in third.
Leaders Torben Grael and Marcelo Ferreira of Brazil are on 13 points and lead second-placed Canada by seven points.