This paper is focused on the structure-properties relationship of synthesized sulfonated poly(aryl sulfone)s comprised of a bulky aliphatic-aromatic structure. Nucleophilic aromatic substitution together with a coupling step was used to prepare random copolymers with excellent film-forming ability. High thermal, mechanical, and dimensional stability of membranes ascribed to the presence of rigid aromatic sections. The oxidative stability of the optimized membrane with a 50% degree of sulfonation (Z-50) was studied in ex-situ and in-situ accelerated degradation tests. The results were evaluated by Fenton test, scanning electron microscope, nuclear magnetic resonance spectrometry, and open-circuit voltage test. The voltage decay of 0.62 mV/h was attained during 100 h open-circuit voltage test at 80 °C under 100% relative humidity. Temperature and relative humidity-dependent impedance and high-frequency resistance of membranes revealed the structural benefit of membranes. Polarization and performance curves of the optimized sample were collected at three temperatures of 80, 100, and 120 °C under 100% relative humidity. The examination of the membrane polarization under 30–100% relative humidity at the temperature of 80 °C showed a current density of about 732.7 mA/cm2 even at 30% relative humidity. The design of such bulky aliphatic-aromatic poly(aryl sulfone) was responsible for this result.