Fiber-to-the-Room (FTTR) has emerged as the core architecture for next-generation home and enterprise networks, offering gigabit-level bandwidth and seamless wireless coverage. However, the complex multi-device topology of FTTR networks presents significant challenges in identifying sources of network performance degradation and conducting accurate root cause analysis. Conventional approaches often fail to deliver efficient and precise operational improvements. To address this issue, this paper proposes a Transformer-based multi-task learning model designed for automated root cause analysis in FTTR environments. The model integrates multidimensional time-series data collected from access points (APs), enabling the simultaneous detection of APs experiencing performance degradation and the classification of underlying root causes, such as weak signal coverage, network congestion, and signal interference. To facilitate model training and evaluation, a multi-label dataset is generated using a discrete-event simulation platform implemented in MATLAB. Experimental results demonstrate that the proposed Transformer-based multi-task learning model achieves a root cause classification accuracy of 96.75%, significantly outperforming baseline models including Long Short-Term Memory (LSTM), Gated Recurrent Unit (GRU), Random Forest, and eXtreme Gradient Boosting (XGBoost). This approach enables the rapid identification of performance degradation causes in FTTR networks, offering actionable insights for network optimization, reduced operational costs, and enhanced user experience.