I tried the new cable from Other World Computing--the one they use for their USB 3.0 drives. It is short and fairly thick, and, I assume, suited for these drives.
I thought the problem had been solved, but today, two days later, I just got the DNEP message while working at the computer actively. I checked the Console messages, and at the same time the DNEP appeared, these messages showed up on the Console. Whether they help in terms of identifying the cause or are simply markers and reports of what happened, I don't know. And other than seeing a reference to the WDC driver, I have no idea what they mean.
11/20/14 3:04:08.149 PM prl_deskctl_agent[27396]: WARNING: The Gestalt selector gestaltSystemVersion is returning 10.9.1 instead of 10.10.1. Use NSProcessInfo's operatingSystemVersion property to get correct system version number.
Call location:
11/20/14 3:04:08.153 PM prl_deskctl_agent[27396]: 0 CarbonCore 0x00007fff87e70dc3 ___Gestalt_SystemVersion_block_invoke + 113
11/20/14 3:04:08.153 PM prl_deskctl_agent[27396]: 1 libdispatch.dylib 0x00007fff88b11c13 _dispatch_client_callout + 8
11/20/14 3:04:08.153 PM prl_deskctl_agent[27396]: 2 libdispatch.dylib 0x00007fff88b11b26 dispatch_once_f + 117
11/20/14 3:04:08.153 PM prl_deskctl_agent[27396]: 3 CarbonCore 0x00007fff87e194da _Gestalt_SystemVersion + 987
11/20/14 3:04:08.153 PM prl_deskctl_agent[27396]: 4 CarbonCore 0x00007fff87e190c7 Gestalt + 144
11/20/14 3:04:08.153 PM prl_deskctl_agent[27396]: 5 prl_deskctl_agent 0x00000001096e493f CMAC_resume + 119183
11/20/14 3:04:08.153 PM prl_deskctl_agent[27396]: 6 prl_deskctl_agent 0x0000000109163709 start + 919369
11/20/14 3:04:08.221 PM com.apple.kextd[21]: ERROR: invalid signature for com.wdc.driver.USB-64HP, will not load
11/20/14 3:04:08.466 PM com.apple.kextd[21]: ERROR: invalid signature for com.wdc.driver.USBHP, will not load
11/20/14 3:04:09.116 PM com.apple.xpc.launchd[1]: (com.apple.mdworker.bundles[27398]) Could not find uid associated with service: 0: Undefined error: 0 507
11/20/14 3:04:09.117 PM com.apple.xpc.launchd[1]: (com.apple.mdworker.bundles) Service only ran for 0 seconds. Pushing respawn out by 10 seconds.
11/20/14 3:04:10.000 PM kernel[0]: jnl: disk2s2: replay_journal: from: 79159296 to: 79785984 (joffset 0x2baa000)
11/20/14 3:04:10.000 PM kernel[0]: jnl: disk2s2: journal replay done.
Now, one would think that Apple engineers could make something out of this. Maybe I should set up an AppleCare incident report. Since I no longer have AppleCare it will cost me $20 or so. If someone here who does have AppleCare active, and who has this problem with a WD External USB 3.0 drive, you might be able to submit this.