<p>A hospital AI triage system may pass procurement review, data protection assessment, clinical safety review, validation, and monitoring, yet continue operating when a serious but inconclusive subgroup concern emerges. This article calls that residual possibility the paradox of governed continuation: ethical concern may be recognised, documented, and escalated without acquiring authority over permission to rely. It develops Authorised Interruption Capability (AIC) as the organisational capability by which ethically salient concern can reach a forum authorised to decide whether reliance should continue unchanged, continue under constraint, pause, roll back, be redesigned, undergo further validation, or be justified. AIC is a domain-specific condition of action-bearing AI governance: recognised ethical concern must acquire timely, proportionate, reason-preserving force before ordinary proof thresholds settle the case. The article contributes to responsible AI governance by specifying this authority relation between recognition and permission to rely, and by showing how existing governance tools should be configured if they are to make concern action-bearing rather than merely recordable.</p>