Environmental stability remains a major challenge for the commercialisation of organic solar cells and degradation pathways remain poorly understood. Designing materials for improved device stability requires an understanding of the relationship between the properties of the donor or acceptor molecule and different degradation mechanisms. Here we study the correlations between various molecular parameters of the fullerene derivative bis-PCBM and the degradation rate of polymer:bis-PCBM organic solar cells, based on the same carbazole-alt-benzothiadiazole polymer, in aerobic and anaerobic conditions. We compare eight high purity bis-PCBM isomers with different electronic, chemical and packing properties along with PCBM and the mixture of bis isomers. In the case of aerobic photodegradation, we find that device degradation rate is positively correlated to the LUMO energy of the bis-PCBM isomer and to the degree of crystallinity of the isomer, while the correlation of degradation with driving force for epoxide formation is unclear. These results support the idea that in these samples, aerobic photodegradation proceeds via superoxide formation by the photogenerated polaron on the fullerene, followed by further chemical reaction. In the absence of air, photodegradation rate is correlated with molecular structure, supporting the mechanism of microstructural degradation via fullerene dimerization. The approach and findings presented here show how control of specific molecular parameters through chemical design can serve as a strategy to enhance stability of organic solar cells.