The durability of polymeric materials is closely linked to their degradation under specific operating conditions when different stressors—general or specific, such as high temperature, sunlight or ionizing radiation, solvents, or mechanical stresses—act simultaneously, causing degradation. In the case of electrical cables, the durability of the electrically insulating materials used in their construction is an important parameter to ensure their operational security. In this work, we studied the degradation state of various types of electrical insulating materials from cables used in particle acceleration systems under European Organization for Nuclear Research (CERN) conditions (e.g., Super Proton Synchrotron, SPS) as a function of time and irradiation dose. A simple kinetic model was proposed based on the exponential decrease in the antioxidant amount in polymeric insulations. The onset oxidation time (OIT) values, used as an indicator of antioxidant concentration, were obtained from isothermal differential scanning calorimetry (DSC) and chemiluminescence (CL) measurements. Fourier transform infrared (FTIR) measurements were used to assess the degradation state and identify polymeric materials. The practical applicability of such a model in diagnosing degradation and in the subsequent evaluation of the remaining service life is of interest, as it can be adapted to a broad range of operating conditions and materials.