1. A computer-implemented method comprising: providing, by one or more computing systems of a configurable network service and for a client of the configurable network service, a first virtual computer network having a first computing node that has an assigned virtual Internet Protocol (IP) address for the first virtual computer network; maintaining, by the one or more computing systems, a second computing node as a replicated copy of the first computing node, the maintaining including updating the second computing node to reflect changes in state of the first computing node as the first computing node runs; determining, by the one or more computing systems, to replace the first computing node in the first virtual computer network with the second computing node; and updating, by the one or more computing systems and in response to the determining, mapping information for the first virtual computer network to associate the second computing node with the virtual IP address assigned to the first computing node.