Cape Town - The Blitzboks went down 21-19 to England on Saturday to leave themselves with little chance of making the semi-finals of the Hamilton Sevens.
South Africa have one pool match left against Kenya on Sunday (01:13, SA time), but victory there is unlikely to help them with only the top-ranked side in each pool progressing to the semi-finals.
Japan are the other side in Pool B.
The early signs were the Blitzboks were on their way to victory when tries from Stedman Gans and JC Pretorius gave them a healthy lead, but England then hit back with three consecutive tries to take a 21-14 lead.
Justin Geduld did score a late try, but when his conversion went wide the Blitzboks had not done enough to save he game.
From there Justin Geduld found a gap to score. But he then missed the decisive conversion from a relatively easy position to leave the Blitzboks on the brink of elimination from the Cup competition.
Earlier in the day, Neil Powell's men beat Japan 35-5 thanks to tries from Angelo Davids (2), Muller du Plessis, Cecil Afrika and JC Pretorius.