Web Inspector attached state is not preserved between browser launches. The problem appeared after http://trac.webkit.org/changeset/56051. CFPreferencesAppSynchronize which store settings to disk is called somewhere inside Safari's code on Windows. I don't have access to it but as an alternative solution I could call it somewhere in WebInspectorClient but it would diverge from the current approach.
Closing as invalid, as this bug pertains to the old inspector UI and/or its tests. Please file a new bug (https://www.webkit.org/new-inspector-bug) if the bug/feature/issue is still relevant to WebKit trunk.