This contribution presents experimental verification of bistability, a special form of local fading memory, in a physical TaOx memristor. System-theoretic methods are applied to the physics-based model of the ReRAM cell under consideration to explore the origin of the local fading memory and its robustness against the intrinsic cycle-to-cycle variability of the device. Multiple real-world measurements are performed to confirm the existence of one separatrix in the transient behavior of the device as a fingerprint of bistability.