The recent advances in Legal Large Language Models (LLMs) have transformed the landscape of legal research and practice by automating tasks, enhancing research precision, and supporting complex decision-making processes. However, effectively adapting LLMs to the legal domain remains challenging due to the complexity of legal reasoning, the need for precise interpretation of specialized language, and the potential for hallucinations. This paper examines the efficacy of Domain-Adaptive Continual Pre-Training (DACP) in improving the legal reasoning capabilities of LLMs. Through a series of experiments on legal reasoning tasks within the Taiwanese legal framework, we demonstrate that while DACP enhances domain-specific knowledge, it does not uniformly improve performance across all legal tasks. We discuss the trade-offs involved in DACP, particularly its impact on model generalization and performance in prompt-based tasks, and propose directions for future research to optimize domain adaptation strategies in legal AI.