FWIW, I have a WD MyBook USB 3.0 1.5 TB external drive connected to a powered (low powered, not high) 3.0 USB hub connected to a MacBook Pro Retina 15" mid-2012 with a recently replaced logic board (because of HDMI problems), using 10.9.3.
I have always had spontaneous disconnects of the external drive. All the WD software has been removed both by their uninstall program and manually for whatever was left. I get these disconnects whether connected to the hub or directly to the USB 3.0 port on the computer, but probably more often with the hub.
Here is the latest Console log of messages before and at the time of the disconnect, and after it reconnected spontaneously. I did have "put hardware to sleep" in the power saving preferences, and I've just unchecked that based on some earlier posts here.
6/19/14 12:56:31.000 PM kernel[0]: disk1s2: media is not present.
6/19/14 12:56:31.000 PM kernel[0]: jnl: disk1s2: do_jnl_io: strategy err 0x6
6/19/14 12:56:31.000 PM kernel[0]: jnl: disk1s2: write_journal_header: error writing the journal header!
6/19/14 12:56:31.000 PM kernel[0]: hfs: unmount initiated on MyBook on device disk1s2
6/19/14 12:56:31.000 PM kernel[0]: jnl: disk1s2: close: journal 0xffffff803846ac20, is invalid. aborting outstanding transactions
6/19/14 12:56:31.000 PM kernel[0]: USBMSC Identifier (non-unique): 5743415A4138363735383138 0x1058 0x1140 0x1025, 3
6/19/14 12:56:31.509 PM fseventsd[76]: disk logger: failed to open output file /Volumes/MyBook/.fseventsd/00000000000bbe06 (No such file or directory). mount point /Volumes/MyBook/.fseventsd
6/19/14 12:56:31.509 PM fseventsd[76]: disk logger: failed to open output file /Volumes/MyBook/.fseventsd/00000000000bbe06 (No such file or directory). mount point /Volumes/MyBook/.fseventsd
6/19/14 12:56:32.639 PM mDNSResponder[66]: ERROR: mDNSPlatformReadTCP - SSLRead: -9806
6/19/14 12:56:32.639 PM mDNSResponder[66]: ERROR: tcpCallback - attempt to read message length failed (-1)
6/19/14 12:56:45.000 PM kernel[0]: jnl: disk1s2: replay_journal: from: 17653760 to: 21299200 (joffset 0x2baa000)
6/19/14 12:56:53.000 PM kernel[0]: jnl: disk1s2: journal replay done.
6/19/14 12:57:00.000 PM kernel[0]: hfs: Removed 0 orphaned / unlinked files and 504 directories
6/19/14 12:57:00.000 PM kernel[0]: hfs: mounted MyBook on device disk1s2
6/19/14 12:57:00.961 PM fseventsd[76]: event logs in /Volumes/MyBook/.fseventsd out of sync with volume. destroying old logs. (14714 15 14714)
6/19/14 12:57:01.369 PM fseventsd[76]: log dir: /Volumes/MyBook/.fseventsd getting new uuid: FE177170-818E-46AB-B21B-6556CEEE75D6
6/19/14 12:59:20.703 PM mdworker32[5665]: CGSConnectionByID: 0 is not a valid connection ID.
6/19/14 12:59:20.704 PM mdworker32[5665]: CGSGetSpaceManagementMode: No connection with id 0x 0
Is there anything in the first part of these messages that gives a clue as to why it disconnected (unmounted)?