Power-logistics scheduling in modern seaports typically follows a predict-then-optimize pipeline. To enhance the decision quality of predictions, decision-focused learning has been proposed, which aligns the training of forecasting models with downstream decision outcomes. However, this end-to-end design inherently restricts the value of forecasting models to a specific task structure and therefore generalizes poorly to evolving tasks induced by varying vessel arrivals. We address this gap with a decision-focused continual learning framework that adapts online to a stream of scheduling tasks. Specifically, we introduce Fisher-information-based regularization to enhance cross-task generalization by preserving parameters critical to prior tasks. A differentiable convex surrogate is also developed to stabilize gradient backpropagation. The proposed approach enables learning a decision-aligned forecasting model across a varying task stream with sustainable long-term computational and memory requirements. Experiments calibrated to Jurong Port show improved decision performance and cross-task generalization over existing methods, together with reduced computational cost and a bounded memory footprint.