The semi-regular variable star V Canum Venaticorum (V CVn) is well-known for its unusual linear polarization position angle (PA). Decades of observing V CVn reveal a nearly constant PA spanning hundreds of pulsation cycles. This phenomenon has persisted through variability that has ranged by 2 magnitudes in optical brightness and through variability in the polarization amplitude over 0.3% and 6.9%. Additionally, the polarization fraction of V CVn varies inversely with brightness. This paper presents polarization measurements obtained over three pulsation cycles. We find that the polarization maximum does not always occur precisely at the same time as the brightness minimum. Instead, we observe a small lead or lag in relation to the brightness minimum, spanning a period of a few days up to three weeks. Furthermore, the PA sometimes exhibits a non-negligible rotation, especially at lower polarization levels. To elucidate the unusual optical behavior of V CVn, we present a list of literature sources that also exhibit polarization variability with a roughly fixed PA. We find this correlation occurs in stars with high tangential space velocities, i.e., "runaway" stars, suggesting that the long-term constant PA is related to how the circumstellar gas is shaped by the star's high-speed motion through the interstellar medium.