The design of novel polymers has brought more attention to bulk heterojunction polymer:fullerene solar cells in the past decade. A typical example is the synthesis, through chemical structure engineering, of the benzodithiophene-co-thieno[3,4-b]thiophene (BDT-TT) polymers leading to power conversion efficiency of over 10%. In this work, we study the stability for a set of PBDT-TT polymers. We conduct a systematic UV-degradation study on the solar cells. Most importantly, the paper shows clearly the effect of polymer chemical structure on the UV-degradation pathway of the solar cells. We find that based on the polymer chemical structure, solar cells of polymers with alkoxy side chains are more stable (20% loss in PCE) than those with alkylthienyl side chains (48% loss in PCE) over the period of study. These findings pave the way for new materials that yield efficient as well as stable organic solar cells.