This study aimed to investigate the degradation of dry biopotential electrodes using the anodic stripping voltammetry (ASV) technique. The electrodes were based on Ti-Cu thin films deposited on different polymeric substrates (polyurethane, polylactic acid, and cellulose) by Direct Current (DC) magnetron sputtering. TiCu0.34 thin films (chemical composition of 25.4 at.% Cu and 74.6 at.% Ti) were prepared by sputtering a composite Ti target. For comparison purposes, a Cu-pure thin film was prepared under the same conditions and used as a reference. Both films exhibited dense microstructures with differences in surface topography and crystalline structure. The degradation process involved immersing TiCu0.34 and Cu-pure thin films in artificial sweat (prepared following the ISO standard 3160-2) for different durations (1 h, 4 h, 24 h, 168 h, and 240 h). ASV was the technique selected to quantify the amount of Cu(II) released by the electrodes immersed in the sweat solution. The optimal analysis conditions were set for 120 s and −1.0 V for time deposition and potential deposition, respectively, with a quantification limit of 0.050 ppm and a detection limit of 0.016 ppm. The results showed that TiCu0.34 electrodes on polyurethane substrates were significantly more reliable over time compared to Cu-pure electrodes. After 240 h of immersion, the TiCu0.34 electrodes released a maximum of 0.06 ppm Cu, while Cu-pure electrodes released 16 ppm. The results showed the significant impact of the substrate on the electrode’s longevity, with cellulose bases performing poorly. TiCu0.34 thin films on cellulose released 1.15 µg/cm2 of copper after 240 h, compared to 1.12 mg/cm2 from Cu-pure films deposited on the same substrate. Optical microscopy revealed that electrodes based on polylactic acid substrates were more prone to corrosion over time, whereas TiCu thin-film metallic glass-like structures on PU substrates showed extended lifespan. This study underscored the importance of assessing the degradation of dry biopotential electrodes for e-health applications, contributing to developing more durable and reliable sensing devices. While the study simulated real-world conditions using artificial sweat, it did not involve in vivo measurements.