This paper investigates physical-layer security for uplink low Earth orbit (LEO) satellite communications in the presence of multiple non-colluding satellite eavesdroppers. Secure beamforming design in such systems is challenging due to time-varying orbital geometry and probabilistic fading-induced outage constraints. To address this, we first derive tractable closed-form expressions for both connection and secrecy outage probabilities under Nakagami-m fading, and develop differentiable upper-bound cost functions that are amenable to optimization. Next, to exploit the predictable orbital dynamics and temporal correlation of satellite mobility, we reformulate the non-convex secrecy rate maximization problem as a constrained Markov decision process. We then develop a primal-dual soft actor-critic algorithm with a multi-head cost critic that jointly optimizes beamforming while enforcing average outage constraints via Lagrangian relaxation. Numerical results show that the proposed framework improves the ergodic secrecy rate over maximum ratio transmission across all eavesdropper configurations, and outperforms zero-forcing in dense eavesdropping regimes. It achieves within 7 percent of an offline successive convex approximation benchmark while requiring only a single forward pass, enabling low-complexity real-time operation. These results indicate that the proposed approach is applicable to secure beamforming in dynamic LEO satellite environments.

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