The durability of the membrane electrode assembly (MEA) is one of the important requirements for the successful commercialization of anion exchange membrane fuel cells (AEMFCs). While chemical stabilities of the components (the catalyst, membrane, and ionomer) have been assessed by ex situ tests, the degradation mode of the components in a single-cell is still not fully understood. Herein, the degradation of a MEA based on an ionomer having a polycarbazole main chain and a trimethyl ammonium side group was systematically investigated for a single-cell level under constant current conditions. The degradations of the catalyst, membrane, and ionomer were compared by in situ electrochemical and ex situ post-mortem analyses. The catalyst and ionomer in the cathode showed significant degradation, whereas the membrane was relatively durable, suggesting that the formation of a strong alkaline environment in the cathode catalyst layer is a major cause of the performance fade. The use of an alkaline-stable ionomer with an N,N-dimethylhexylamine group, which is designed based on density functional theory (DFT) calculations, in the cathode catalyst layer leads to 87% durability improvement. This work enhances the understanding of the key factors affecting the durability of AEMFCs under real operation and suggests practical strategies toward higher durability.