Herein, we utilize organic radical scavengers to mitigate the chemical degradation of polymer membranes without sacrificing their proton conductivity. Several hydrocarbon composite membranes based on sulfonated poly(arylene ether sulfone) (SPES50, degree of sulfonation = 50%) and containing organic radical scavengers were prepared and characterized in terms of water uptake, ion-exchange capacity, proton conductivity, and oxidative stability, being additionally exposed to hydrogen peroxide for accelerated oxidative stability testing. Precise analysis of the molecular weight and its distribution before and after the above test confirmed that the incorporation of radical scavengers enhanced the chemical durability of membranes while maintaining their proton conductivity. Finally, in an accelerated open circuit voltage durability test, composite membranes showed lifetimes exceeding 1400 h, whereas pristine SPES50 failed after 750 h. On the basis of the above, organic radical scavengers were concluded to be superior to those based on transition-metal compounds, not engaging in any interactions with the sulfonate groups of the membrane polymer and hence not compromising their proton conductivity.