Adapting Large Language Models for recommendation (LLM4Rec)has garnered substantial attention and demonstrated promising results. However, the challenges of practically deploying LLM4Rec are largely unexplored, with the need for incremental adaptation to evolving user preferences being a critical concern. Nevertheless, the suitability of traditional incremental learning within LLM4Rec remains ambiguous, given the unique characteristics of LLMs. In this study, we empirically evaluate the commonly used incremental learning strategies (full retraining and fine-tuning) for LLM4Rec. Surprisingly, neither approach leads to evident improvements in LLM4Rec's performance. Rather than directly dismissing the role of incremental learning, we ascribe this lack of anticipated performance improvement to the mismatch between the LLM4Recarchitecture and incremental learning: LLM4Rec employs a single adaptation module for learning recommendation, hampering its ability to simultaneously capture long-term and short-term user preferences in the incremental learning context. To validate this speculation, we develop a Long- and Short-term Adaptation-aware Tuning (LSAT) framework for LLM4Rec incremental learning. Instead of relying on a single adaptation module, LSAT utilizes two adaptation modules to separately learn long-term and short-term user preferences. Empirical results demonstrate that LSAT could enhance performance, validating our speculation.