Reinforcement learning with verifiable rewards (RLVR) has emerged as a powerful paradigm for improving reasoning capabilities. However, training RLVR with Mixture-of-Experts (MoE) policies remains fragile and is often prone to reward collapse.We identify a MoE-specific source of instability, referred to as router shift (RS), where changes in expert routing across policy updates exacerbate off-policy mismatch. This effect leads to increasingly volatile importance-ratio signals and bursty clipping behavior, which consistently precede training collapse.Motivated by this diagnosis, we propose Router-Shift Policy Optimization (RSPO). RSPO computes a per-token router-shift ratio conditioned on the previously activated experts, applies stop-gradient and a lower-bound floor, and softly rescales importance ratios prior to clipping and aggregation. This design explicitly accounts for routing-induced distributional drift during off-policy optimization.We evaluate the effect of RSPO under two settings: a synthetic countdown task and real-world reasoning tasks on MATH and Code. Across both settings, RSPO achieves better performance and exhibits greater stability compared to recent MoE-based RLVR methods.