A security tag assembly structured to discourage unauthorized removal of merchandise comprising a base including at least one magnetomechanical member normally operatively oriented in an armed mode. The armed mode is at least partially defined by the magnetomechanical member demonstrating a vibration or mechanical resonance when exposed to a predetermined resonant frequency, such as when passing through or otherwise disposed in proximity to a monitoring alarm assembly. A stabilizing assembly comprising at least one stabilizing magnet is disposed and structured to expose said magnetomechanical member to a stabilizing magnet field sufficient operative characteristics to facilitate restoration or maintenance of the armed mode of the magnetomechanical member even when exposed to a disruptive magnetic field, such as when the magnetomechanical member is attempting to be disarmed by an unauthorized source.