1. A non-transitory computer-accessible storage medium storing program instructions, wherein the program instructions are executable by each of a plurality of nodes of a cluster of virtual servers, wherein each node of the cluster of virtual servers executes virtualization software which implements a virtualization environment in which one or more virtual server machines execute; wherein the program instructions are executable by one or more processors of a first node of the cluster of virtual servers to: register to receive notifications of one or more types of configuration changes in the virtualization environment of the first node, wherein each respective type of configuration change prevents the first node from responding to broadcast messages sent by other nodes of the cluster of virtual servers during the respective type of configuration change; after registering to receive the notifications, receive a first notification indicating that a first type of configuration change in the virtualization environment of the first node has been initiated; and in response to the first notification, transmit a first message to one or more other nodes of the cluster of virtual servers to inform the one or more other nodes that the first node is in a temporarily inactive state in which the first node is unable to respond to broadcast messages sent by other nodes of the cluster of virtual servers; wherein, for each respective node of the one or more other nodes, the program instructions are executable by one or more processors of the respective node to store information indicating that the first node is in the temporarily inactive state in response to receiving the first message.