Recent health system shocks such as the Ebola disease outbreak have focused global health attention on the notion of resilient health systems. In this commentary, we reflect on the current framing of the concept of resilience in health systems discourse and propose a reframing. Specifically, we propose that: (1) in addition to sudden shocks, health systems face the ongoing strain of multiple factors. Health systems need the capacity to continue to deliver services of good quality and respond effectively to wider health challenges. We call this capacity everyday resilience; (2) health system resilience entails more than bouncing back from shock. In complex adaptive systems (CAS), resilience emerges from a combination of absorptive, adaptive and transformative strategies; (3) nurturing the resilience of health systems requires understanding health systems as comprising not only hardware elements (such as finances and infrastructure), but also software elements (such as leadership capacity, power relations, values and appropriate organizational culture). We also reflect on current criticisms of the concept of resilient health systems, such as that it assumes that systems are apolitical, ignoring actor agency, promoting inaction, and requiring that we accept and embrace vulnerability, rather than strive for stronger and more responsive systems. We observe that these criticisms are warranted to the extent that they refer to notions of resilience that are mismatched with the reality of health systems as CAS. We argue that the observed weaknesses of resilience thinking can be addressed by reframing and applying a resilience lens that is better suited to the attributes of health systems as CAS.