When a buoyant bubble is inserted into a closed capillary that is slightly smaller than the capillary length, it appears stuck; exactly why this is so is a puzzle that has remained unanswered over the past 50 years. Recent calculations suggest that the bubble's motion is critically dependent on the hydrodynamics of the surrounding liquid film; however, quantitative measurements of these dynamics are lacking. We provide direct measurements of the dynamics of the liquid film surrounding a “stuck” bubble, recorded using interference microscopy. The film slowly relaxes to a constant thickness, and is stabilized by disjoining pressure at long times. The film's stability at this thickness is demonstrated by recovery after applied thermal perturbations; thus, we confirm that Bretherton's buoyant bubble is not pinned at a contact line, but is instead ostensibly stuck by extraordinarily slow flow in the surrounding liquid film whose thickness is set by a balance of capillary stress and disjoining pressure.