The mechanical recycling of styrenic polymers from waste electrical and electronic equipment (WEEE) is often limited by thermomechanical degradation occurring during repeated processing. In this work, the degradation behaviour of acrylonitrile–butadiene–styrene (ABS) recovered from sorted WEEE streams was systematically investigated through multiple extrusion cycles, and the effectiveness of antioxidant stabilization was evaluated. Progressive degradation was assessed by chemical structure, rheological, thermal and mechanical testing, and colorimetric analysis. Repeated processing resulted in increased melt flow, altered viscoelastic behaviour, molecular weight reduction, deterioration of mechanical properties, and discoloration. To mitigate these effects, antioxidant-stabilized compounds were prepared and subjected to identical reprocessing pathways. The addition of antioxidants effectively reduced chain scission, stabilized rheological properties, and limited colour changes during reprocessing. Furthermore, the processability of the optimized recycled ABS is demonstrated through filament extrusion for fused filament fabrication, highlighting its potential for high-value additive manufacturing applications. These results demonstrate that appropriate stabilization strategies can significantly enhance the process stability and recyclability of styrenic polymers from WEEE streams, supporting their use in higher-value applications within a circular economy framework.