Thin-laminate composites with thicknesses below 200 mu m hold significant promise for future, larger, and lighter deployable structures. This paper presents a study of the time-dependent failure behavior of thin carbon-fiber laminates under bending, focusing on establishing a fundamental material-level understanding of this type of failure. A novel test method was developed, enabling in-situ micro-CT imaging during long-term bending. Time-to-rupture experiments revealed the stochastic nature of failure, prompting a statistical approach to account for initial imperfections. The total probability of failure was calculated using separate Weibull functions for instantaneous and delayed time-dependent failures. The resulting function, dependent on curvature and aging time, is a design guideline for the design of future deployable space structures. Time-lapse micro-CT imaging identified kink bands and fiber-matrix debonding as primary failure mechanisms, providing essential insights for the design optimization of composite laminates.