We investigate the relationship between structure and robustness in the metabolic networks of Escherichia coli, Methanosarcina barkeri, Staphylococcus aureus, and Saccharomyces cerevisiae, using a cascading failure model based on a topological flux balance criterion. We find that, compared to appropriate null models, the metabolic networks are exceptionally robust. Furthermore, by decomposing each network into rigid clusters and branched metabolites, we demonstrate that the enhanced robustness is related to the organization of branched metabolites, as rigid cluster formations in the metabolic networks appear to be consistent with null model behavior. Finally, we show that cascading in the metabolic networks can be described as a percolation process.