The two top teams of the three pools will qualify for the quarter-finals and the two best third-place finishers will complete the top eight in the knock-out phase for the podium.
A 10-5 defeat to Ireland was followed by a 17-5 loss to New Zealand and although highly competitive on defence in both matches, the Blitzboks' attack lacked spark, mainly due to limited attacking opportunities and field position.
In both clashes, brave defence delivered a tight contest, but the lack of ball in hand cost the attack-minded SA side dearly.
In their opening match against Ireland, dogged defence by South Africa in the first half kept the Irish at bay. Ireland held possession for the opening six minutes of the half, but hardly made headway against a well-organised defensive line.
South Africa could not slow down the Irish efficiently enough to make any turnovers and something finally had to give. Irish winger Jordon Conroy scored on the buzzer to hand Ireland a 5-0 lead at the break.
The second half was as tight, but the Blitzboks had more ball in hand and looked dangerous on attack. A yellow card to Ryan Oosthuizen for a high tackle gave Ireland the one-man advantage they needed to score a second try.
The Springbok Sevens team, now with urgency on attack, managed a late try, but ran out of time to score a second try.
Against New Zealand, it was pretty much the same. Moses Leo scored first for New Zealand, but Sevyn Davids levelled the scores. South Africa lost their main striking weapon on attack, Quewin Nortje, early in the half and that did not help their efforts.
New Zealand scored a late try in the first half for a 10-5 lead and added a converted try in the second to edge out a brave Blitzboks effort.
South Africa play Japan at 16h00 on Thursday and need a big win to stay in contention for the quarter finals and some results in other pools going their way.
Scorers:
South Africa 5 (0), Ireland 10 (5)
SA - Try: Selvyn Davids
Ireland - Tries: Jordan Conroy, Terry Kennedy.
South Africa 5 (5), New Zealand 17 (10)
SA – Try: Selvyn Davids
NZ – Tries: Moses Leo (2), Ngarohi McGarvey-Black. Conversion: Akuila Rokolisoa.