Rich again gained valuable Olympic Quota Allocation List points for the second week in a row, following her 21st place performance last week in Kreischberg, Austria.
Two heats with 25 athletes in each group competed with the aim of placing in the top six to advance to the 12 woman final. Riders had two runs, with the highest scoring counting towards their final ranking.
Rich narrowly missed out on the top six, finishing in tenth place, with her highest score coming in her first run, where the judges awarded her a total score of 52.50 points.
After combining the places of both heats, Rich had a final overall placing of 20th.
The event was won by Enni Rukajarvi of Finland, with Anna Gasser of Austria in second and American Jamie Anderson third
NSWIS rider Matthew Cox also competed in Laax, finishing in 58th place.