I have had the same issue with My Passport since upgrading to Mountain Lion.
I found this support issue on this site:
http://www.wdc.com/wdproducts/wdsmartwareupdate/firmware.asp?id=wdfMP_Essential&os=MAC
However when I went to upgrade the firmware as suggested by this ticket, WD’s firmware upgrade crashed (see crash notes below). There’s nothing wrong with the volume - both DiskUtility and WD’s own SmartWare disk verifier gave the volume a clean bill of health. (And BTW, the firmware upgrade was unsigned, so I had to lower my security settings just to launch the firmware.)
Crash Notes when running WDFirmwareUpdater on Macbook Air 2011 running Mountain Lion:
Process: WDFirmwareUpdater [5933]
Path: /Users/USER/Downloads/WDFirmwareUpdater.app/Contents/MacOS/WDFirmwareUpdater
Identifier: com.yourcompany.WDFirmwareUpdater
Version: 3.1.0.10 (3.1.0.10)
Code Type: X86 (Native)
Parent Process: launchd [181]
User ID: 501
Date/Time: 2012-08-15 14:36:32.040 -0400
OS Version: Mac OS X 10.8 (12A269)
Report Version: 10
Interval Since Last Report: 65265 sec
Crashes Since Last Report: 7
Per-App Interval Since Last Report: 113 sec
Per-App Crashes Since Last Report: 3
Anonymous UUID: E2FD3614-28DB-4F3F-A985-69F9FC0ACDC4
Crashed Thread: 11
Exception Type: EXC_BREAKPOINT (SIGTRAP)
Exception Codes: 0x0000000000000002, 0x0000000000000000
Application Specific Information:
*** Terminating app due to uncaught exception ‘NSInvalidReceivePortException’, reason: ‘connection went invalid while waiting for a reply’
Application Specific Backtrace 1:
0 CoreFoundation 0x92ab07ab __raiseError + 219
1 libobjc.A.dylib 0x98033602 objc_exception_throw + 230
2 CoreFoundation 0x92a1023b +[NSException raise:format:] + 139
3 Foundation 0x935c419f -[NSConnection sendInvocation:internal:] + 2310
4 Foundation 0x935c3710 -[NSDistantObject forwardInvocation:] + 386
5 CoreFoundation 0x929fcc50 ___forwarding___ + 896
6 CoreFoundation 0x929fc862 _CF_forwarding_prep_0 + 50
7 WDFirmwareUpdater 0x00007b14 -[WDFirmwareUpdate runDevicePlugin] + 204
8 Foundation 0x935ac318 -[NSThread main] + 45
9 Foundation 0x935ac29b __NSThread__main__ + 1396
10 libsystem_c.dylib 0x92843557 _pthread_start + 344
11 libsystem_c.dylib 0x9282dcee thread_start + 34