Rapid advancements in speech synthesis and voice conversion bring convenience but also new security risks, creating an urgent need for effective audio deepfake detection. Although current models perform well, their effectiveness diminishes when confronted with the diverse and evolving nature of real-world deepfakes. To address this issue, we propose a continual learning method named Region-Based Optimization (RegO) for audio deepfake detection. Specifically, we use the Fisher information matrix to measure important neuron regions for real and fake audio detection, dividing them into four regions. First, we directly fine-tune the less important regions to quickly adapt to new tasks. Next, we apply gradient optimization in parallel for regions important only to real audio detection, and in orthogonal directions for regions important only to fake audio detection. For regions that are important to both, we use sample proportion-based adaptive gradient optimization. This region-adaptive optimization ensures an appropriate trade-off between memory stability and learning plasticity. Additionally, to address the increase of redundant neurons from old tasks, we further introduce the Ebbinghaus forgetting mechanism to release them, thereby promoting the capability of the model to learn more generalized discriminative features. Experimental results show our method achieves a 21.3% improvement in EER over the state-of-the-art continual learning approach RWM for audio deepfake detection. Moreover, the effectiveness of RegO extends beyond the audio deepfake detection domain, showing potential significance in other tasks, such as image recognition. The code is available at https://github.com/cyjie429/RegO