I as well am seeing this problem with both the Win8 client and Win Server 2012. Snips from the WindowsUpdate.log from both are below:
Win8
2012-07-17 09:16:24:830
956 dd4
PT +++++++++++ PT: Synchronizing server updates +++++++++++
2012-07-17 09:16:24:830
956 dd4
PT + ServiceId = {7971F918-A847-4430-9279-4A52D1EFE18D}, Server URL = https://fe1.update.microsoft.com/v6/ClientWebService/client.asmx
2012-07-17 09:16:24:965
956 dd4
WS WARNING: Nws Failure: errorCode=0x803d0014
2012-07-17 09:16:24:965
956 dd4
WS WARNING: Original error code: 0x80072efe
2012-07-17
09:16:24:965 956
dd4 WS
WARNING: There was an error communicating with the endpoint at 'https://fe1.update.microsoft.com/v6/ClientWebService/client.asmx'.
2012-07-17 09:16:24:965
956 dd4
WS WARNING: There was an error sending the HTTP request.
2012-07-17 09:16:24:965
956 dd4
WS WARNING: The connection with the remote endpoint was terminated.
2012-07-17 09:16:24:965
956 dd4
WS WARNING: The connection with the server was terminated abnormally
2012-07-17 09:16:24:965
956 dd4
WS WARNING: Web service call failed with hr = 80240440.
2012-07-17 09:16:24:965
956 dd4
WS WARNING: Current service auth scheme='None'.
2012-07-17 09:16:24:965
956 dd4
WS WARNING: Proxy List used: '(null)', Bypass List used: '(null)', Last Proxy used: '(null)', Last auth Schemes used: 'None'.
2012-07-17 09:16:24:965
956 dd4
WS FATAL: OnCallFailure(hrCall, m_error) failed with hr=0x80240440
2012-07-17 09:16:24:965
956 dd4
PT WARNING: PTError: 0x80240440
2012-07-17 09:16:24:965
956 dd4
PT WARNING: GetConfig_WithRecovery failed: 0x80240440
2012-07-17 09:16:24:965
956 dd4
PT WARNING: RefreshConfig failed: 0x80240440
2012-07-17 09:16:24:965
956 dd4
PT WARNING: RefreshPTState failed: 0x80240440
2012-07-17 09:16:24:965
956 dd4
PT WARNING: Sync of Updates: 0x80240440
2012-07-17 09:16:24:965
956 dd4
PT WARNING: SyncServerUpdatesInternal failed: 0x80240440
2012-07-17 09:16:24:965
956 dd4
Agent * WARNING: Failed to synchronize, error = 0x80240440
2012-07-17 09:16:24:967
956 dd4
Agent * WARNING: Exit code = 0x80240440
2012-07-17 09:16:24:967
956 dd4
Agent *********
2012-07-17 09:16:24:967
956 dd4
Agent ** END ** Agent: Finding updates [CallerId = AutomaticUpdates]
2012-07-17 09:16:24:967
956 dd4
Agent *************
2012-07-17 09:16:24:967
956 dd4
Agent WARNING: WU client failed Searching for update with error 0x80240440
2012-07-17 09:16:24:968
956 d3c
AU >>## RESUMED ## AU: Search for updates [CallId = {89C7EF38-9F3B-4A8F-A308-7C6A0625578A} ServiceId = {7971F918-A847-4430-9279-4A52D1EFE18D}]
2012-07-17 09:16:24:968
956 d3c
AU # WARNING: Search callback failed, result = 0x80240440
2012-07-17 09:16:24:968
956 d3c
AU #########
2012-07-17 09:16:24:968
956 d3c
AU ## END ## AU: Search for updates [CallId = {89C7EF38-9F3B-4A8F-A308-7C6A0625578A} ServiceId = {7971F918-A847-4430-9279-4A52D1EFE18D}]
2012-07-17 09:16:24:968
956 d3c
AU #############
2012-07-17 09:16:24:968
956 d3c
AU All AU searches complete.
2012-07-17 09:16:24:968
956 d3c
AU # WARNING: Failed to find updates with error code 80240440
2012-07-17 09:16:24:968
956 d3c
AU Need to show Unable to Detect notification
Server 2012:
2012-07-17 09:40:46:381
880 840
PT +++++++++++ PT: Synchronizing server updates +++++++++++
2012-07-17 09:40:46:381
880 840
PT + ServiceId = {7971F918-A847-4430-9279-4A52D1EFE18D}, Server URL = https://fe1.update.microsoft.com/v6/ClientWebService/client.asmx
2012-07-17 09:40:46:466
880 840
WS WARNING: Nws Failure: errorCode=0x803d0014
2012-07-17 09:40:46:466
880 840
WS WARNING: Original error code: 0x80072efe
2012-07-17
09:40:46:466 880
840 WS
WARNING: There was an error communicating with the endpoint at 'https://fe1.update.microsoft.com/v6/ClientWebService/client.asmx'.
2012-07-17 09:40:46:466
880 840
WS WARNING: There was an error sending the HTTP request.
2012-07-17 09:40:46:466
880 840
WS WARNING: The connection with the remote endpoint was terminated.
2012-07-17 09:40:46:466
880 840
WS WARNING: The connection with the server was terminated abnormally
2012-07-17 09:40:46:466
880 840
WS WARNING: Web service call failed with hr = 80240440.
2012-07-17 09:40:46:466
880 840
WS WARNING: Current service auth scheme='None'.
2012-07-17 09:40:46:466
880 840
WS WARNING: Proxy List used: '(null)', Bypass List used: '(null)', Last Proxy used: '(null)', Last auth Schemes used: 'None'.
2012-07-17 09:40:46:466
880 840
WS FATAL: OnCallFailure(hrCall, m_error) failed with hr=0x80240440
2012-07-17 09:40:46:466
880 840
PT WARNING: PTError: 0x80240440
2012-07-17 09:40:46:466
880 840
PT WARNING: GetConfig_WithRecovery failed: 0x80240440
2012-07-17 09:40:46:466
880 840
PT WARNING: RefreshConfig failed: 0x80240440
2012-07-17 09:40:46:466
880 840
PT WARNING: RefreshPTState failed: 0x80240440
2012-07-17 09:40:46:467
880 840
PT WARNING: Sync of Updates: 0x80240440
2012-07-17 09:40:46:467
880 840
PT WARNING: SyncServerUpdatesInternal failed: 0x80240440
2012-07-17 09:40:46:467
880 840
Agent * WARNING: Failed to synchronize, error = 0x80240440
2012-07-17 09:40:46:469
880 840
Agent * WARNING: Exit code = 0x80240440
2012-07-17 09:40:46:469
880 840
Agent *********
2012-07-17 09:40:46:469
880 840
Agent ** END ** Agent: Finding updates [CallerId = AutomaticUpdates]
2012-07-17 09:40:46:469
880 840
Agent *************
2012-07-17 09:40:46:469
880 840
Agent WARNING: WU client failed Searching for update with error 0x80240440
2012-07-17 09:40:46:470
880 b8c
AU >>## RESUMED ## AU: Search for updates [CallId = {12123DBF-F1C2-4FCC-B6DF-23409AE3AFB9} ServiceId = {7971F918-A847-4430-9279-4A52D1EFE18D}]
2012-07-17 09:40:46:470
880 b8c
AU # WARNING: Search callback failed, result = 0x80240440
2012-07-17 09:40:46:470
880 b8c
AU #########
2012-07-17 09:40:46:470
880 b8c
AU ## END ## AU: Search for updates [CallId = {12123DBF-F1C2-4FCC-B6DF-23409AE3AFB9} ServiceId = {7971F918-A847-4430-9279-4A52D1EFE18D}]
2012-07-17 09:40:46:470
880 b8c
AU #############
2012-07-17 09:40:46:470
880 b8c
AU All AU searches complete.
2012-07-17 09:40:46:470
880 b8c
AU # WARNING: Failed to find updates with error code 80240440
2012-07-17 09:40:46:470
880 b8c
AU Need to show Unable to Detect notification