Currently, various rescue robots are developed to use them at a disaster site. It is suggested that legged-robots are useful on uneven and fragile terrain because a legged-robot can choose a grounding point discretely. In the previous study, leg-grope movement was proposed for a quadruped robot walking on fragile terrain. However, the walking experiment by using the leg-grope movement was carried out only for one cycle of walking gait, and the possibility of continuous walk that using the leg-grope movement has not analyzed yet. In this paper, we studied whether the leg-grope movement can be carried out continuously or not. As a result, we found the region for the leg-grope movement will never extend in future steps. Therefore, once the region for the leg-grope movement becomes small, the region cannot recover its groping area. The proposed leg-grope movement has to satisfy severe condition for a quadruped robot to walk continuously.