Can't access Windows Internal Database in SQL Server 2008 - login fails

Trying to recover some disk space by shrinking the size of our WSUS database, or at least figure out why it's so big, I tried to connect to the Windows Internal Database in SQL Server Management Studio (using the \.\pipe\mssql$microsoft##ssee\sql\query database name I've seen referenced in multiple places) and got an error: Cannot connect to \.\pipe\mssql$microsoft##ssee\sql\query.

Login failed for user '[ourdomain]/[myusername]'. (Microsoft SQL Server, Error: 18456)

Server Name: \.\pipe\mssql\$microsoft##ssee\sql\query

Error Number: 18456

Severity: 14

State: 1

Line Number: 65536

My account has domain administrator privileges, so I don't understand why it wouldn't work. The help link it gives me says that "If your error indicates state 1, contact your SQL Server administrator" (who, unfortunately, is me).

I also tried the WsusDBMaintenance script from here, which should apparently just work, and got the same "Login failed for user" message.

Update: I found the corresponding entries in the error log, which say:

2009-10-09 14:13:51.30 Logon       Error: 18456, Severity: 14, State: 11.
2009-10-09 14:13:51.30 Logon       Login failed for user '[domain]\[user]'. [CLIENT: <named pipe>]

It says here that state 11 = "Valid login but server access failure".

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I'm doing a little tour of questions that relate to WID on Windows 2008 to note that Windows 2012 changes the pipe to \\.\pipe\MICROSOFT##WID\tsql\query –  Richard Gadsden Dec 11 '12 at 15:02