1. A system, comprising: a plurality of compute nodes, configured to implement: a plurality of hosts for virtual compute instances; a control plane; the control plane, configured to: for a virtual compute instance operating at a source host that is identified for live migration to a destination host and is a client of a network-based storage resource that stores data for which access is limited to the source host: pause operation of the virtual compute instance at the source host upon preparation of the destination host for operation of the virtual compute instance; modify the access to the data stored by the network-based storage resource to limit the access to the data stored by the network-based storage resource to the destination host of the virtual compute instance instead of the source host of the virtual compute instance; and resume operation of the virtual compute instance at the destination host.