Multimodal large language models (MLLMs) have shown strong performance in perception and question-answering, but many clinical decisions require reasoning across observations collected over time rather than from a single input. We study this problem in longitudinal modeling, where evidence evolves across visits. We introduce LUMINA (LongitUdinal MultImodal reasoNing Agent), a single-agent framework that incrementally builds an auditable evidence state before making predictions. Instead of predicting directly from all observations, LUMINA organizes current evidence, compares observations across prior visits, maintains longitudinal memory, optionally retrieves relevant cross-subject summaries, and verifies whether the accumulated evidence supports the final decision. We evaluate LUMINA on two subject-level benchmarks: Alzheimer’s disease classification and 36-month progression forecasting from observed visit prefixes. Across nine MLLM backbones, LUMINA consistently outperforms MLLM baselines and an adapted medical reasoning agent, achieving 13.8%–18.5% relative balanced accuracy gains on classification and 16.8%–24.8% gains on progression forecasting over the strongest non-agent baseline. Additional evaluations preserve the same method ordering on Parkinsonian-state classification and breast cancer treatment-response prediction.