A binaural hearing system includes first and second hearing devices communicatively coupled by way of a binaural communication link. The first hearing device determines that a signal quality measure of a wireless signal transmitted by the remote audio source is greater than an upper threshold level. In response, both hearing devices enter a wireless audio rendering mode in which they render a remote audio stream from the remote audio source to a user. While operating in the wireless audio rendering mode, both hearing devices determine that a signal quality measure of the remote audio stream drops below a lower threshold level. In response to this determination, both hearing devices exit the wireless audio rendering mode.