This paper focuses on six-degree-of-freedom (six-DOF) spatial cable-suspended parallel robots with eight cables (8-6 CSPRs) because the redundantly actuated CSPRs are relevant in many applications, such as large-scale assembly and handling tasks, and pick-and-place operations. One of the main concerns for the 8-6 CSPRs is the stability because employing cables with strong flexibility and unidirectional restraint operates the end-effector of the robot under external disturbances. As a consequence, this paper attempts to address two key issues related to the 8-6 CSPRs: the force-pose stability measure method and the stability sensitivity analysis method. First, a force-pose stability measure model taking into account the poses of the end-effector and the cable tensions of the 8-6 CSPR is presented, in which two cable tension influencing factors and two position influencing factors are developed, while an attitude influence function representing the influence of the attitudes of the end-effector on the stability of the robot is constructed. And furthermore, a new type of workspace related to the force-pose stability of the 8-6 CSPRs is defined and generated in this paper. Second, a force-pose stability sensitivity analysis method for the 8-6 CSPRs is developed with the gray relational analysis method, where the relationship between the force-pose stability of the robot and the 14 influencing factors (the end-effector’s poses and cable tensions) is investigated to reveal the sequence of the 14 influencing factors on the force-pose stability of the robot. Finally, the proposed force-pose stability measure method and stability sensitivity analysis method for the 8-6 CSPRs are verified through simulations.