A computing system that provides virtual computing services may generate and manage remote computing sessions between client computing devices and virtual desktop instances hosted on the service provider's network. A computing resource instance manager may monitor connections to and disconnections from a virtual desktop instance during particular time periods, and may apply a resource management policy to determine whether and when to shut down an underlying virtualized computing resource instance following a disconnection (e.g., immediately, after some period of time, or only between certain hours). A storage volume for the virtual desktop instance may be detached during a shutdown. In response to a reconnection request, the virtualized computing resource instance (or another such instance) may be restarted and the storage volume may be reattached. The computing resource instance manager may develop a model for predicting when to shut down or restart an instance based on historical data or machine learning.