The performance of global Internet communication is significantly influenced by the reliability and the stability of Internet routing systems, especially the Border Gateway Protocol (BGP), the de facto standard for inter-domain routing. In this paper, we investigate the reliability of BGP sessions and the Internal BGP (IBGP) networks in the environment of unreliable physical and routing layers. The reliability analysis of IBGP networks is difficult, because IBGP sessions may be correlated to each other by the shared underlying physical links and TCP enables IBGP sessions to tolerate certain level of network failures. In this paper, we first investigate the failure probability of IBGP sessions and its relation to BGP timers and TCP retransmission behaviors. The result of this investigation is a simple modification of TCP that increases the robustness of IBGP sessions significantly. Second, we present a novel reliability model to measure the resilience of the whole IBGP networks. This model is of great importance for studying the function loss of IBGP operations and it also provides the theory basis for IBGP network optimization in terms of reliability.