Robustness, fault tolerance, and long lifetime are key requirements of sensor networks used in real-world applications. Dense sensor networks with high sensor redundancy offer the possibility of redundant sensing and low duty-cycle operation at the same time, thus the required robust sensing services can be provided along with elongated lifetime. In this paper the Controlled Greedy Sleep Algorithm is analyzed. With low local communication overhead the proposed algorithm is able to solve the k-coverage sensing problem while it effectively preserves energy in the network. In addition, it can adapt to dynamic changes in the network such as node failures. The quality of service (network-wide k-coverage) is guaranteed independently of communication errors in the network (as long as it is physically possible); message losses affect only the network lifetime. Node failures may cause temporary decrease in the coverage service. The robustness of the algorithm is proven and its behavior is illustrated by simulation examples.