This study presents the improved stabilization effects of graphene on a polymer substrate, namely a styrene-isoprene-styrene triblock copolymer (SIS) which creates opportunities for long-term applications and radiation processing. The added graphene has a remarkable activity on the protection of polymer against their oxidation due to the penetration of free macroradical fragments into the free interlayer space. The chemiluminescence procedure used for the evaluation of the progress of oxidation reveals the delaying effect of oxidative degradation by the doubling extension of oxidation induction time, when the material formulation containing graphene is oxidized at 130 °C. The pristine polymer that is thermally aged requires an activation energy of 142 kJ mol−1, while the modified material needs 148, 158 and 169 kJ mol−1, for the oxidative degradation in the presence of 1, 2 and, respectively, 3 wt% of graphene. The contribution of graphene content (1 wt%) on the stability improvement of SIS is demonstrated by the increase of onset oxidation temperature from 190 °C for neat polymer to 196 °C in the presence of graphene and to 205 °C for the polymer stabilized with graphene and rosemary extract. The addition of graphene into the polymer formulations is a successful method for enlarging durability instead of the modification of receipt with synthesis antioxidants. The presumable applications of these studied materials cover the areas of medical wear, food packaging, commodities, sealing gaskets and others that may also be included through the products for nuclear power plants.