1. Launch Spotlight Client, Go to Configure | Diagnostic Server | Configure the use of Extended Events
2. Uncheck 'Use Extended Events' checkbox
3. After you turn off Extended Events you can look at the sessions on those instances and see if there are old Spotlight sessions, then try to kill them.
4. If the session that hangs cannot be killed, then you can resolve the timeout issue by restarting the instance.
The SQL Server 2008 R2 Service Pack 2 should solve this. It can be downloaded here