An exemplary method includes a stream management system that detects a request for any device included in a media processing system to receive a media stream provided by a television service. In response, the stream management system determines that a digital video recording (“DVR”) device included in the media processing system is already receiving and recording a maximum number of media streams that the DVR device is allowed to concurrently record. In response to this determination, the stream management system performs a status check with respect to the media streams being received and recorded by the DVR device in order to determine whether one of the media streams may be dropped by the DVR device so that the DVR device can instead receive and record the media stream identified in the request. Corresponding systems and methods are also described.