Anomalously enhanced fast‐electron losses are observed on relativisticElayers in the RECE‐Christa device when the applied toroidal magnetic field decreases to zero in times shorter than ring lifetime. These losses consistently occur in a certain region of the field‐reversal parameter and the ratio of applied toroidal to axial magnetic fields at the ring position. The critical parameter range is independent of the radial gradient of the applied mirror field, the background gas pressure, and the rate‐of‐decay ofB&thgr;; however, it depends on the axial length of the rings, and there may be a threshold indB&thgr;/dt. The observed parameter dependence as well as the absence of any kink or tilt motions point to new orbital resonances as the cause of these losses.