A client device implements a streaming client and a proxy server. The proxy server intercepts one or more playlist requests from the streaming client directed to one or more network servers external to the client device. Responsive to interception of a sliding-window playlist request of a particular type, the proxy server generates a corresponding on-demand playlist request. The intercepted sliding-window playlist request and the corresponding on-demand playlist request are sent from the proxy server to the one or more network servers. The proxy server receives an on-demand playlist from the one or more network servers responsive to the on-demand playlist request, and generates a local copy of the on-demand playlist. A current version of the local copy of the on-demand playlist is subsequently provided by the proxy server to the streaming client responsive to interception in the proxy server of a request from the streaming client for the on-demand playlist.