In this paper, we explore the impact of wireless channel capacity on asymptotic detection performance for distributed detection in wireless sensor networks (WSNs). As a key performance metric for large-scale WSNs, the asymptotic detection performance is characterized by the error exponents of detection error probabilities. In particular, we consider error exponents under dependent observations and nonideal channels. We derive a sufficient condition under which the detection system will result in zero error exponents under both orthogonal channels and multiple-access channels. We show that if the channel capacity is zero, the corresponding error exponents become zero as well. In addition, a special case of dependent observations where sensor measurements are independently identically distributed given a hidden variable or vector is studied. Under this model, we further derive the necessary and sufficient condition for having zero error exponents. Numerical examples are also presented to validate the results and demonstrate the relationship among the asymptotic detection performance and system parameters.