Large Language Model (LLM) serving is increasingly constrained by the growing size of the key-value (KV) cache, which scales with both context length and generation length. Prior work shows that attention is dominated by a small subset of critical tokens, yet existing systems struggle to exploit this efficiently without degrading accuracy, especially in long generation. We make a key observation: the temporal stability of these critical tokens varies significantly across KV heads: some heads consistently focus on the same tokens, while others shift frequently. Building on this insight, we introduce FlexiCache, a hierarchical KV-cache management system that leverages the temporal stability of KV heads to reduce GPU memory usage and computation overhead, while preserving model accuracy. FlexiCache classifies KV heads as stable or unstable: it retains all KV-cache pages from unstable heads in GPU memory, whereas for stable heads, it keeps only the top-K pages on the GPU and offloads the rest to host memory. By exploiting temporal stability, FlexiCache performs periodic reranking for stable heads to fetch newly promoted top pages. Implemented atop vLLM, FlexiCache reduces GPU memory footprint for long-context requests by up to 70%, improves offline serving throughput by 1.38-1.55x, and lowers online token latency by 1.6-2.1x, all while maintaining accuracy in long-context, long-generation scenarios.