In one aspect, a computer-implemented method for preventing centrifugal clutch lock-ups within a work vehicle transmission may generally include transmitting a signal associated with disengaging a clutch of the transmission, wherein the clutch includes a hydraulic actuator having a pressure relief valve. The method may also include monitoring a pressure of the hydraulic fluid supplied to the actuator relative to a predetermined pressure threshold and monitoring a rotational speed of a clutch can associated with the clutch relative to a predetermined speed threshold, wherein the speed threshold is defined relative to a lock-up speed associated with the clutch can. In addition, the method may include transmitting a lock-up signal associated with limiting the rotational speed of the clutch can and/or providing an indication that a clutch lock-up is likely to occur when the pressure exceeds the pressure threshold and the rotational speed exceeds the speed threshold.