Mobile sensor networks (MSNs) have emerged from the interaction between mobile robotics and wireless sensor networks. MSNs can be deployed in harsh environments, where failures in some nodes can partition MSNs into disconnected network segments or reduce the coverage area. A k-connected network can tolerate at least k-1 arbitrary node failures without losing its connectivity. In this study, we present a coverage-aware distributed k-connectivity maintenance (restoration) algorithm that generates minimum-cost movements of active nodes after a node failure to preserve a persistent k value subject to a coverage conservation criterion. The algorithm accepts a coverage conservation ratio (as a trade-off parameter between coverage and movements) and facilitates coverage with the generated movements according to this value. Extensive simulations and testbed experiments reveal that the proposed algorithm restores k-connectivity more efficiently than the existing restoration algorithms. Furthermore, our algorithm can be utilized to maintain k-connectivity without sacrificing the coverage, significantly.