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This paper aims to address distributed event-triggered learning-based secure control for multiple battery energy storage systems (BESSs) under persistent false-date injection (FDI) attacks. To tackle FDI attacks and also save communication resources, a distributed learning-based secure control based on a dynamic event-triggered framework is established. This control scheme uses an adaptive law to update the estimation matrix for a neural network (NN) approximator, using only relative state variables at triggered instants. To ensure uniform boundedness of all variables involved in the update law, a proper projection operator is introduced. Additionally, the updated law incorporates a low-pass filter structure, which can suppress unfavorable high-frequency oscillations when a high-gain learning rate is applied. It is rigorously proven that under such distributed event-triggered learning-based control protocols, frequency regulation, active power sharing, and SoC balancing can be achieved with arbitrary accuracy by adjusting the learning rates and control parameters. Finally, real-time simulations of the IEEE 57-bus system are performed using OPAL-RT to illustrate the efficacy of the developed learning strategy.