Rotation-invariant (RI) point cloud models aim to reduce sensitivity to viewpoint changes, but their performance still drops noticeably in real-world settings when local geometry is degraded by noise, occlusion, and uneven sampling. Once these disturbances propagate through deeper layers, they can lead to significant robustness degradation, especially for high-capacity RI backbones. To address this problem, we propose AGSM-CPA (Adaptive Geometric Signal Modulation with Cross-Perturbation Alignment), a lightweight and plug-and-play framework that enhances the robustness of RI models without altering their core convolutional operators. It integrates two complementary modules: the Geometric Signal-to-Noise Ratio (G-SNR) modulation mechanism, which adaptively suppresses unreliable neighborhoods based on local coordinate variance, and the Cross-Perturbation Semantic Consistency Alignment (CP-SCL) module, which enforces prediction consistency between weakly augmented inputs and strongly corrupted ones. We evaluate AGSM-CPA on ModelNet40, ScanObjectNN, and ShapeNetPart. Across standard corruption protocols, AGSM-CPA consistently improves robustness while maintaining competitive clean accuracy with negligible computational overhead. These results indicate that AGSM-CPA offers a practical, reliability-aware adapter for robust rotation-invariant point cloud learning.