5G networks offer exceptional reliability and availability, ensuring consistent performance and user satisfaction. Yet they might still fail when confronted with the unexpected. A resilient system is able to adapt to real-world complexity, including operating conditions completely unanticipated during system design. This makes resilience a vital attribute for communication systems that must sustain service in scenarios where models are absent or too intricate to provide statistical guarantees. Such considerations indicate that artifical intelligence (AI) will play a major role in delivering resilience. In this paper, we examine the challenges of designing AIs for resilient radio access networks, especially with respect to unanticipated and rare disruptions. Our theoretical results indicate strong limitations of current statistical learning methods for resilience and suggest connections to online learning and causal inference.