Next-generation visual assistants, such as smart glasses, embodied agents, and always-on life-logging systems, must reason over an entire day or more of continuous visual experience. In ultra-long video settings, relevant information is sparsely distributed across hours or days, making memory a fundamental challenge: models must accumulate information over time, recall prior states, track temporal order, and abstract recurring patterns. However, existing week-long video benchmarks are primarily designed for perception and recognition, such as moment localization or global summarization, rather than reasoning that requires integrating evidence across multiple days. To address this gap, we introduce EgoMemReason, a comprehensive benchmark that systematically evaluates week-long egocentric video understanding through memory-driven reasoning. EgoMemReason evaluates three complementary memory types: entity memory, tracking how object states evolve and change across days; event memory, recalling and ordering activities separated by hours or days; and behavior memory, abstracting recurring patterns from sparse, repeated observations over the whole week period. EgoMemReason comprises 500 questions across three memory types and six core challenges, with an average of 5.1 video segments of evidence per question and 25.9 hours of memory backtracking. We evaluate EgoMemReason on 17 methods across MLLMs and agentic frameworks, revealing that even the best model achieves only 39.6% overall accuracy. Further analysis shows that the three memory types fail for distinct reasons and that performance degrades as evidence spans longer temporal horizons, revealing that long-horizon memory remains far from solved. We believe EgoMemReason establishes a strong foundation for evaluating and advancing long-context, memory-aware multimodal systems.