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Existing self-evolving approaches address this gap by updating prompts, memory, or model weights, but none directly repair the symbolic structures that encode how tasks are executed, and few provide the governance guarantees required for safe deployment. We introduce ANNEAL, a neuro-symbolic agent that converts recurring failures into governed symbolic edits of a process knowledge graph without modifying foundation model weights. Its core mechanism, Failure-Driven Knowledge Acquisition (FDKA), localizes the responsible operator, synthesizes a typed patch through constrained LLM generation, and validates the proposal via multi-dimensional scoring, symbolic guardrails, and canary testing before commit. 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Its core mechanism, Failure-Driven Knowledge Acquisition (FDKA), localizes the responsible operator, synthesizes a typed patch through constrained LLM generation, and validates the proposal via multi-dimensional scoring, symbolic guardrails, and canary testing before commit. 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