This paper presents an adaptive visual servoing framework for robotic on-orbit servicing (OOS), specifically designed for capturing tumbling satellites. The vision-guided robotic system is capable of selecting optimal control actions in the event of partial or complete vision system failure, particularly in the short term. The autonomous system accounts for physical and operational constraints, executing visual servoing tasks to minimize a cost function. A hierarchical control architecture is developed, integrating a variant of the Iterative Closest Point (ICP) algorithm for image registration, a constrained noise-adaptive Kalman filter, fault detection and recovery logic, and a constrained optimal path planner. The dynamic estimator provides real-time estimates of unknown states and uncertain parameters essential for motion prediction, while ensuring consistency through a set of inequality constraints. It also adjusts the Kalman filter parameters adaptively in response to unexpected vision errors. In the event of vision system faults, a recovery strategy is activated, guided by fault detection logic that monitors the visual feedback via the metric fit error of image registration. The estimated/predicted pose and parameters are subsequently fed into an optimal path planner, which directs the robot's end-effector to the target's grasping point. This process is subject to multiple constraints, including acceleration limits, smooth capture, and line-of-sight maintenance with the target. Experimental results demonstrate that the proposed visual servoing system successfully captured a free-floating object, despite complete occlusion of the vision system.