An intelligent Real-Time Sensing (RTS) system must continuously acquire, update, integrate, and apply knowledge to adapt to real-world dynamics. Managing distributed intelligence in this context requires Federated Continual Learning (FCL). However, effectively capturing the diverse characteristics of RTS data in FCL systems poses significant challenges, including severely impacting computational and communication resources, escalating energy costs, and ultimately degrading overall system performance. To overcome these challenges, we investigate how the data distribution shift from ideal to practical RTS scenarios affects Artificial Intelligence (AI) model performance by leveraging the \textit{generalization gap} concept. In this way, we can analyze how sampling time in RTS correlates with the decline in AI performance, computation cost, and communication efficiency. Based on this observation, we develop a novel Sample-driven Control for Federated Continual Learning (SCFL) technique, specifically designed for mobile edge networks with RTS capabilities. In particular, SCFL is an optimization problem that harnesses the sampling process to concurrently minimize the generalization gap and improve overall accuracy while upholding the energy efficiency of the FCL framework. To solve the highly complex and time-varying optimization problem, we introduce a new soft actor-critic algorithm with explicit and implicit constraints (A2C-EI). Our empirical experiments reveal that we can achieve higher efficiency compared to other DRL baselines. Notably, SCFL can significantly reduce energy consumption up to $85\%$ while maintaining FL convergence and timely data transmission.