1. A system, comprising: one or more computing devices, comprising: one or more processors; and a memory comprising program instructions that when executed on the one or more processing cause the one or more computing devices to: monitor respective health status information of a plurality of compute instances of a virtual computing service of a provider network, wherein a subset of the compute instances are hosted at one or more instance hosts mounted at a first server rack; detect, based on an analysis of the health status information, that one or more rack-level failure events affecting the subset of the compute instances at the first server rack have occurred; in response to a determination, that the particular compute instance meets an acceptance criterion for a failure-induced migration to a different server rack: identify a target instance host, mounted at a second server rack of the provider network, to which the particular compute instance is to be migrated; and initiate one or more configuration operations to re-launch the particular compute instance at the target instance host; wherein the acceptance criterion is based, as least in part on: an analysis of storage-related operations requested from a particular compute instance of the subset prior to the one or more rack-level failure events; and a determination of whether state information of the particular compute instance is saved at a local storage device affected by the one or more rack-level failure events.