This paper focuses on the design of robust IBGP route reflection networks, which are very important to the reliability and stability of Internet. A new approach is proposed to calculate the failure probability of IBGP sessions based on the probability distribution of IGP routing recovery time. To measure the robustness of IBGP, a new metric: TS (traffic sensitivity) is presented. Based on this metric, the optimization problem of finding the most robust IBGP route reflection topologies is investigated, in which a cluster is allowed to have one or more redundant route reflectors and the maximum number of IBGP sessions a router can have is limited. The relationship between the route reflectors redundancy and the robustness is discussed, and the lower bound of this problem optimization is given. And for a special case that there is a redundant route reflector within each cluster, the solvability conditions for the problem are given and it is shown that the problem in general is NP-hard.