Since access to the Tivoli management region logs using the desktop GUI is from the discovered object, if discovery fails there is no way to get to that log from the desktop.
Resolving the problem
The Manage Tivoli Logs task is designed to run against an application object so it can filter the set of logs that is displayed to the task logs against that object as well as the "utility" logs. If there is no object to run the task against on the endpoint, it is not possible to get the logs from that endpoint by using this task. In this situation, access the endpoint system by some other method and examine the discovery logs that way.