While Large Language Model (LLM) agents increasingly rely on long-term memory for persistent interactions, the retrieval mechanisms governing this memory are rarely treated as evolvable components. This static approach limits performance on heterogeneous memory queries, which often demand diverse evidence construction strategies. To address this, we introduce \textbf{ERSkill}, a retrieval-centric framework for self-evolving, skill-guided memory access. ERSkill compiles interaction histories into a structured memory store and represents retrieval behaviors as executable skills composed of fundamental primitives. At inference time, a trained router dynamically matches each query to the optimal skill to construct tailored evidence for answer generation. To enable continuous improvement, ERSkill co-evolves the skill set and the router during training. It employs an experience trie to efficiently record explored retrieval paths, alongside a double-frontier mechanism that safely decouples the expansion of new skill capabilities from stable, router-facing deployment. Experiments across multiple agent memory benchmarks demonstrate that ERSkill substantially outperforms strong non-evolving and self-evolving baselines. Notably, it improves the overall average across F1, BLEU-1, and LLM-judge scores by 31.3\% with Qwen3-Next-80B-A3B-Instruct and by 28.1\% with GPT-5.4-nano.