The current document is directed to automated application-release-management facilities that, in a described implementation, coordinate continuous development and release of cloud-computing applications. The application-release-management process is specified, in the described implementation, by application-release-management pipelines, each pipeline comprising one or more stages, with each stage comprising one or more tasks. The currently described methods and systems check whether endpoints and external tasks are reachable prior to initiating execution of application-release-management pipelines. Automatic reachability checking is scheduled for idle intervals, when the workflow-execution-engine component of the automated application-release-management facility is not executing release pipelines.