Omnidirectional gimbal systems use multiple actuators to achieve the desired line-of-sight (LOS) motion through thrust allocation. However, actuator degradation caused by thermal effects or aging alters the force constants, leading to model mismatch and diminished torque realization performance. Conventional pseudoinverse-based thrust allocation assumes constant actuator characteristics and, therefore, cannot effectively compensate for these variations. This paper proposes an adaptive thrust allocation algorithm based on Recursive Least Squares (RLS) for omnidirectional gimbal systems. The proposed method estimates the force constant of each actuator in real-time using measured torque and actuator current data. These estimated force constants are incorporated into the thrust allocation process to address actuator degradation. Additionally, a weighted thrust allocation strategy redistributes current demand to alleviate the burden on degraded actuators while maintaining the required torque. The proposed algorithm was validated through MATLAB/Simulink simulations under conditions of asymmetric actuator degradation. Compared to the conventional pseudoinverse-based method, the proposed algorithm reduced the torque realization RMSE by 99% and the LOS tracking RMSE by 24.5%. Furthermore, the weighted thrust allocation decreased the RMS current of the most degraded actuator by 35.8%, all while preserving torque realization and LOS tracking performance, demonstrating the effectiveness of the proposed method.