Apparatus, and an associated method, by which to facilitate re-establishment of a traffic channel upon which to communicate pursuant to a communication session, such as a push-to-talk communication session, with a mobile station. The mobile station is maintained in a non-slotted, or other higher-power, mode subsequent to release of a traffic channel to facilitate speedy re-establishment of the traffic channel upon a request for the re-establishment. A selector selects a time period during which the mobile station is maintained in the mode, and a notification message is generated for communication to a network part of the radio communication system to identify the time period.