Reinforcement learning (RL) algorithms such as PPO and GRPO are widely used to train large language models (LLMs) for multi-turn agentic tasks. However, in off-policy training pipelines, these methods often exhibit unstable optimization dynamics and are prone to performance collapse. Through empirical analysis, we identify two fundamental sources of instability in this setting: (1)~a granularity mismatch between token-level policy optimization and turn-structured interactions, and (2) high-variance and unreliable gradient updates induced by off-policy importance sampling and inaccurate advantage estimation. To address these challenges, we propose SORL, \underline{S}tabilizing \underline{O}ff-Policy \underline{R}einforcement \underline{L}earning for Long-Horizon Agent Training. SORL introduces principled mechanisms that align policy optimization with the structure of multi-turn interactions and adaptively suppress unreliable off-policy updates, yielding more conservative and robust learning dynamics. Within this framework, we instantiate two stabilized algorithms: SO-PPO and SO-GRPO. Both algorithms are designed to mitigate gradient variance and prevent optimization collapse without requiring careful early stopping or heuristic tuning. We evaluate SO-PPO and SO-GRPO on a range of multi-turn search benchmarks, including general question answering, multi-hop question answering, and medical multiple-choice QA tasks. Experimental results show that both methods consistently prevent training instabilities and performance collapses observed in standard PPO and GRPO, maintain lower clipping ratios and more stable optimization trajectories, and achieve superior or comparable task performance. These results demonstrate that the proposed algorithm provides a practical, scalable, and general framework for stabilizing reinforcement learning in multi-turn LLM agent training.