Large Language Models (LLMs) are increasingly deployed as continuously evolving services, where frequent base-model updates may invalidate previously deployed task-specific Low-Rank Adaptation (LoRA) adapters. For service providers managing numerous downstream model services, retraining each LoRA adapter from scratch for every updated base model is computationally prohibitive and delays service rollout. Meanwhile, the simpler alternative, i.e., naively applying the original LoRA adapter to the updated base model, often leads to degraded service quality due to adapter-backbone incompatibility. To address this problem, we propose ReLoRA, a knowledge-reusing re-adaptation framework that efficiently restores service-ready LoRA adapters for evolving LLM services while preserving or improving task performance. Specifically, ReLoRA comprises two key optimization steps: 1) Adaptive LoRA initialization leverages Bayesian optimization to construct a compatibility-aware starting point by fusing information from both the previously deployed task adapter and the base model's evolution; 2) Fine-tuning with scheduled regularization first rapidly steers the adapter to a high-quality region via strong regularization, followed by relaxed regularization for task-specific refinement. This design enables rapid service-quality recovery with reduced re-adaptation overhead. Extensive experiments demonstrate that ReLoRA reduces time-to-readiness by up to 8.9$\times$ and improves accuracy by up to 4.6\% compared to baselines.