Genetic robustness characterizes the constancy of the phenotype in face of heritable perturbations. Previous investigations have used comprehensive single and double gene knockouts to study gene essentiality and pairwise gene interactions in the yeast Saccharomyces cerevisiae. Here we conduct an in silico multiple knockout investigation of a flux balance analysis model of the yeast's metabolic network. Cataloging gene sets that provide mutual functional backup, we identify sets of up to eight interacting genes and characterize the 'k robustness' (the depth of backup interactions) of each gene. We find that 74% (360) of the metabolic genes participate in processes that are essential to growth in a standard laboratory environment, compared with only 13% previously found to be essential using single knockouts. The genes' k robustness is shown to be a solid indicator of their biological buffering capacity and is correlated with both the genes' environmental specificity and their evolutionary retention.