Cooperative localization is fundamental to autonomous multirobot systems, but most algorithms couple inter-robot communication with observation, making these algorithms susceptible to failures in both communication and observation steps. To enhance the resilience of multirobot cooperative localization algorithms in a distributed system, we use covariance intersection to formalize a localization algorithm with an explicit communication update and ensure estimation consistency at the same time. We investigate the covariance boundedness criterion of our algorithm with respect to communication and observation graphs, demonstrating provable localization performance under even sparse communications topologies. We substantiate the resilience of our algorithm as well as the boundedness analysis through experiments on simulated and benchmark physical data against varying communications connectivity and failure metrics. Especially when inter-robot communication is entirely blocked or partially unavailable, we demonstrate that our method is less affected and maintains desired performance compared to existing cooperative localization algorithms.