What role could AI — especially large language models (LLMs) — play in the work of maintaining software systems? This keynote examines how we can boost the reasoning capabilities of LLMs across three essential maintenance activities: coding, critiquing, and curing software. The first part focuses on code, exploring how we can improve code generation by distilling and utilizing structured reasoning traces inspired by software development practices. The second part addresses critique, illustrating how AI can reason about software vulnerabilities by learning from contrastive reasoning pairs that distinguish valid and flawed explanations. The third part turns to cure, highlighting recent advances that expand the search for fixes using diverse inputs and multi-stage reasoning signals. Across these tasks, we show how advancing LLM reasoning requires data-centric innovations — enriching, linking, and transforming software artefacts to better support structured, task-specific reasoning. The talk concludes with a brief reflection on the road ahead and open questions for future exploration.