The layer-by-layer (LbL) assembly technique has emerged as a versatile and cost-effective method for surface modification, gaining significant widespread attention across various applications. This study evaluates the physicochemical and electrochemical properties of Nafion-based LbL membranes, N117-(PEI/GO)n, incorporating polyethylenimine (PEI) and graphene oxide (GO), and their stability in acidic and oxidative environments of vanadium redox flow battery (VRFB) catholytes. The LbL membranes were subjected to normal (0.1 M VO$_2$$^+$ in 3.0 M H$_2$SO$_4$) and accelerated (1.5 M VO$_2$$^+$ in 3.0 M H$_2$SO$_4$) degradation for 60 days. Analysis revealed notable changes in the physicochemical properties, with diminished peaks for PEI and GO in the Fourier-transform infrared (FTIR) spectrum and weight loss up to 9.9%. Raman spectroscopy further supported these findings, showing a reduction in the intensity of the characteristic D and G bands, which indicates partial degradation of the GO layers after immersion, particularly under accelerated conditions. Meanwhile, the electrochemical properties exhibited significant changes in ion exchange capacity (IEC), which increased by 7%, proton conductivity rose by 41%, and vanadium permeability increased by 762% under accelerated conditions. These changes were attributed to the hydrolysis and oxidation of PEI and GO, driven by highly oxidizing VO$_2$$^+$ ions and acidic conditions, which weakened electrostatic and chemical interactions in the LbL structure. A plausible degradation mechanism was proposed to illustrate the membrane degradation behavior, along with several potential strategies to enhance membrane performance in VRFB operation.