Kenya Sevens team failed to pick any win in their opening two matches of the Las Vegas leg on Saturday morning at the Sam Boyd Stadium, USA.
Shujaa went down 24-7 to New Zealand in their Pool C opener before playing out a 14-14 draw against Argentina in a thrilling second match.
The results leaves Kenya with a mountain to climb if they are to make the cup quarters.
They play Russia on Sunday at 1.12 am in their final pool match.
Against the All Blacks, Kenya let slip a 7-5 half time lead as New Zealand improved in the second half to claim maximum points.
The All Blacks dominated early proceedings and took the lead when Sherwin Stowers landed the game’s first try.
The resulting conversion was however unsuccessful. New Zealand were reduced to six men after Lopu Iopu was sin binned.
Kenya would eventually find their footing as the half wore on and World Rugby Series all-time top scorer Collins Injera raced clear to restore parity and Eden Agero duly converting to give Kenya a 7-5 lead at the drinks.
Kenya were unable to press home their numerical advantage and were made to pay as three second half strikes from Tim Mikkelson, Dylan Collier and Sione Molia alongside two conversions propelled the All Blacks to victory.
In their second match, Kenya raced to a 7-0 lead in the opening minutes thanks to a try from Nelson Oyoo with Agero again spot on on his conversion.
Shujaa were however unable to hold on to the lead as the South Americans hit back with two converted tries from 19 year-old Mathias Oscadzuk to lead 14-7 at halftime.
The second half was end-to-end action with both teams showing flashes of brilliance.
Injera found his way to the try line for his 24th try and Agero again stepped up to convert to level the scores.
Kenya piled the pressure late on but were unable to find the winning try and now face an uphill task to reach the Cup last eight.
New Zealand beat Russia 19-5 in their second match while earlier Argentina thrashed the Europeans 43-0.