Same occurred to me this evening ... no VMs running at the time. Quitting Parallels stopped the log messages from occurring, and restarting Parallels directly did not cause the issue to appear again. Still have to manually delete the log file ... Sad to see this has not been fixed in over two years. Running PD 10.4.0 (29337) on OSX 10.11.4. I was working in OmniGraffle at the time, so I assume some object I put in the clipboard caused the bug.
The logs looked like this before the event. You can see the transition right at the bottom. A full six minutes went by after a successful log rotation before Parallels started complaining about the clipboard. It seems not to be able to handle error conditions very well ....
06-07 02:13:31.946 F /gui:664:160b/ localhost: received result for [DspCmdSendClientStatistics]. RC = [PRL_ERR_SUCCESS]
06-07 02:13:31.946 F /gui:664:160b/ localhost: received result for [DspCmdSendClientStatistics]. RC = [PRL_ERR_SUCCESS]
06-07 02:13:32.112 F /disp:818:2203/ DAILY TIMESTAMP: 2016-06-07 02:13:32 ( version = 10.4.0-29337 ), node_hwid = 'e621585111f9528f87ad80c703dfa924'
06-07 02:13:32.112 F /disp:818:2203/ launchd_mode = 'off'
06-07 02:13:32.237 F /disp:818:172eb/ Task '14Task_LogRotate' with uuid = {b5fa4e28-1c37-42b7-bb67-0daeee4b610a} was started. Flags = 0
06-07 02:13:37.327 F /disp:818:172eb/ Task '14Task_LogRotate' with uuid = {b5fa4e28-1c37-42b7-bb67-0daeee4b610a} was finished with result PRL_ERR_SUCCESS (0) )
06-07 02:16:29.833 F /gui:664:160b/ localhost: sending [DspCmdSendClientStatistics] request...
06-07 02:16:29.834 D /disp:818:300b/ Processing command 'DspCmdSendClientStatistics' 2132 (PJOC_UNKNOWN)
06-07 02:16:29.839 F /gui:664:160b/ localhost: sending [DspCmdSendClientStatistics] request...
06-07 02:16:29.881 F /gui:664:160b/ localhost: sending [DspCmdSendClientStatistics] request...
...
06-07 02:16:30.367 F /gui:664:160b/ localhost: sending [DspCmdSendClientStatistics] request...
06-07 02:16:30.373 F /gui:664:160b/ localhost: sending [DspCmdSendClientStatistics] request...
06-07 02:16:30.380 F /gui:664:160b/ localhost: received result for [DspCmdSendClientStatistics]. RC = [PRL_ERR_SUCCESS]
06-07 02:16:30.380 F /gui:664:160b/ localhost: received result for [DspCmdSendClientStatistics]. RC = [PRL_ERR_SUCCESS]
...
06-07 02:16:30.424 F /gui:664:160b/ localhost: received result for [DspCmdSendClientStatistics]. RC = [PRL_ERR_SUCCESS]
06-07 02:16:30.429 F /gui:664:160b/ localhost: received result for [DspCmdSendClientStatistics]. RC = [PRL_ERR_SUCCESS]
06-07 03:13:32.129 F /disp:818:172a7/ Task '14Task_LogRotate' with uuid = {46de479f-acd0-4f3c-9f0c-1eb638c93aea} was started. Flags = 0
06-07 03:13:37.226 F /disp:818:172a7/ Task '14Task_LogRotate' with uuid = {46de479f-acd0-4f3c-9f0c-1eb638c93aea} was finished with result PRL_ERR_SUCCESS (0) )
06-07 03:19:47.680 W CPTOOL /gui:664:160b/ PasteboardGetItemIdentifier with status=-25131
06-07 03:19:48.073 W CPTOOL /gui:664:160b/ PasteboardGetItemIdentifier with status=-25131