In clinical practice, modality missingness is a common phenomenon due to various factors. However, most mainstream multimodal brain tumor segmentation methods typically assume that the input multimodal data is complete. When certain modalities are missing, the performance of these methods often degrades significantly, resulting in inaccurate segmentation outcomes. To address the limitations of MBDRes-UNet in handling missing modalities, we propose an improved approach named MBDR-V2, which aims to enhance robustness and segmentation performance in practical applications. The architecture of MBDR-V2 consists of three main components. First, a modality-specific encoder, which incorporates the multi-branch adaptive dilated convolutional residual blocks introduced in MBDRes-UNet, is used to construct four independent encoders. These encoders extract unique modality-specific features while maintaining a lightweight design. Second, the modality-correlated encoder, in which we propose a modality association module. This module integrates the spatial features of different tumor regions with modality-specific features sensitive to these regions through a pre-decoding process. Additionally, at each stage of the modality association module, we introduce segmentation-based regularizers, allowing each encoder to learn fully discriminative features to address the training imbalance caused by missing modalities. Finally, an MBDR decoder is employed to achieve end-to-end segmentation. Extensive experiments conducted on the BraTS 2020 dataset demonstrate that MBDR-V2 outperforms MBDRes-UNet and surpasses state-of-the-art methods for incomplete modality segmentation tasks.