Cancer survivors face elevated rates of depression, anxiety, and general emotional distress, yet the precise moments they most need support are often the moments when self-report is sparse, a phenomenon we term the diary paradox. Passive smartphone sensing offers a continuous, unobtrusive alternative, but prior sensing-based affect prediction has been limited by an accuracy ceiling, suggesting a bottleneck not only in available data, but in how behavioral signals are interpreted. We present PULSE, a system that shifts from fixed feature pipelines to agentic sensing investigation: LLM agents equipped with eight purpose-built tools autonomously query smartphone sensing data, compare current behavior against personalized baselines, and calibrate inferences through retrieval-augmented population-level comparisons. Rather than receiving pre-formatted feature summaries, agents decide which modalities to inspect, how far back to look, and how deeply to investigate, mirroring hypothesis-driven clinical reasoning. We evaluate PULSE through a 2*2 factorial design crossing reasoning architecture (structured vs. agentic) with data modality (sensing-only vs. with diary) on 50 cancer survivors from a longitudinal study of cancer survivors. Agentic reasoning is the primary driver of performance: agentic multimodal agent achieves balanced accuracy of 0.743 for emotion regulation desire with diary and sensing data, while agentic agents predict intervention availability at 0.713 with passive sensing data only. These results suggest that agentic investigation may be a cornerstone for unlocking the clinical value of passive sensing, advancing the feasibility of proactive just-in-time mental health support.