Liver surface landmark detection is a fundamental prerequisite for anatomical guidance in laparoscopic liver surgery. However, it remains unreliable in practice due to two pervasive challenges: illumination attenuation in underexposed regions and the structural mismatch between pixel-wise localization and continuous curvilinear geometry. To address these limitations, we propose A2ONet, an attenuation-resilient alternating optimization network for robust liver landmark detection. To mitigate illumination attenuation, A2ONet embraces an illumination field compensation (IFC) block that adaptively enhances dark regions while preserving structural consistency. Meanwhile, we introduce a lightweight frequency-orientation selective filter (FOSF) to suppress repetitive texture interference and preserve salient curvilinear cues. Building upon these resilient representations, we design an alternating seg-curve optimization (ASCO) decoder that iteratively couples dense segmentation with explicit curve modeling, enabling mutual guidance to optimize both structural continuity and endpoint localization. Extensive evaluations on L3D-2K, L3D, and P2ILF demonstrate consistent improvements over competitive methods, establishing a more reliable foundation for intraoperative anatomy guidance. Our code will be available at https://github.com/hyperiondk115/A2ONet.