Large language models (LLMs) have demonstrated strong capabilities in simulating social roles and generating human-like behaviors. However, their effectiveness in predicting real-world user behavior under continuous memory accumulation remains largely unexplored. Most existing studies focus on short-term interactions or static personas, neglecting the dynamic nature of users' historical experiences in social media environments. To address this gap, we introduce FineRob, a novel dataset for fine-grained behavior prediction of social media users, which includes long-term memory traces from 1,866 users across three platforms. Each behavior is decomposed into three elements: object, type, and content, resulting in 78.6k QA records.We identify that as memory accumulates, prediction accuracy drops significantly due to the model's difficulty in accessing detailed historical information. We further propose the OM-CoT fine-tuning framework to enhance the model's ability to process and utilize long-term memory. Experimental results show that our method effectively reduces the performance degradation caused by memory growth, improving fine-grained behavior prediction. \footnote{Code and dataset are available at \url{https://anonymous.4open.science/r/FineRob-791B/}}.