Many countries carried out the research on vertical take-off and vertical landing reusable launch vehicle (RLV) in recent years. The touchdown stability of the RLV when landing vertically on the platform is a key issue for the RLV reuse. Since the structural scheme of the RLV has not been completed in the initial stage of design, and there are no detailed dynamic models for touchdown stability analysis, it is difficult to carry out the dynamic simulation of landing process, therefore the research on estimation method of landing stability is needed. Based on the generalized impact law, this paper analyzes the multiple impacts between the RLV and the landing platform in a two-dimensional landing mode, and the tangential restitution coefficients is given by Coulomb friction model at the impulse level. Firstly, the admissible domain of restitution coefficients in the general motion mode is given through the energetic constraint and unilateral constraints, and the admissible domain of restitution coefficients in two typical motion modes is given as well. Secondly, considering the role of buffer in the landing leg, the collision between the RLV and the platform is approximated as a completely inelastic collision, and accordingly the kinematic restitution coefficients is obtained. Therefore, combined with the kinematic analysis and energy method, a touchdown stability criterion is proposed, which discriminates whether an RLV will fall or not after impacts the platform. In the end, taking an RLV landing prototype as an example, the effects of some key parameters on touchdown stability are analyzed, including the touchdown velocity, the span of supporting leg and the friction coefficient between supporting leg and platform. The results show that the touchdown stability criterion proposed in this paper, is more accurate than the energy method, and the coupling relationship between touchdown velocity, angular velocity and friction coefficient can be considered.