In the heterogeneous networks (HetNets), co-channel interference is a serious problem. Coordinated multi-point (CoMP) transmission has emerged as a powerful technique to mitigate co-channel interference. However, all CoMP techniques rely on information exchange through reliable control channels, which are unlikely to be available in HetNets. In this paper, we study the effect of unreliable control channels, consisting of the access links and backhaul links, on the performance of CoMP. A control channel model is introduced by assigning link failure probability (LFP) to backhaul and access links for the cooperative clusters. Three CoMP architectures, namely the centralized, semi-distributed, and fully distributed are analyzed. We investigate the probability of deficient control channels reducing quality of service and impeding transmission. General closed form expressions are derived for the probability of a cooperative transmission node staying silent in a resource slot due to unreliable control links. By evaluating the average sum rate of users within a CoMP cluster, we show that the performance gains offered by CoMP quickly diminish, as the unreliability of the control links grows.