Detecting depression through social media is a complex task, as noisy user-generated content creates significant interference between persistent depressive patterns and transient emotional expressions. Two main challenges arise: First, negative mood indicators are not exclusive to depressed individuals, making it difficult to distinguish between pathological symptoms and situational emotional variations. Second, existing static models fail to adapt to diverse user expression styles and effectively filter out confounding noise from posts by non-depressed individuals. This results in conventional approaches either overfitting to superficial emotional cues or overlooking subtle long-term symptom progression. To address these issues, we propose the Adversarial Learning Enhanced Stability-aware Routing Transformer for Adaptive Depression Detection(ALERT), a novel framework integrating adaptive attention routing and adversarial learning to enhance robustness against confounding mood signals. Specifically, ALERT employs a stability-aware dynamic routing mechanism to annotate user-specific mood valence trends, providing a structured representation of affective progression over time. An adversarial learning module then leverages these mood-based representations to distinguish between expressions indicative of persistent depressive mood and variations in situational mood states, ensuring adaptability to diverse user behaviors. Experimental results on public social media datasets demonstrate that ALERT outperforms state-of-the-art methods in depression detection, effectively reducing false alarm from transient mood states and improving classification accuracy.