Bonjour,
Comme je m'y attendais un peu le MAC s'est mis en route à 2h pile. 
Par contre, la console m'affiche des messages différents des autres jours. Peut-être que la solution se trouve dedans. 
Ci-desous les messages d'une séquence :
21/04/2016 02:00:01,000    kernel[0]    RTC: Maintenance 2016/4/21 00:00:00, sleep 2016/4/20 20:48:37
21/04/2016 02:00:01,000    kernel[0]    AirPort_Brcm43xx:

owerChange: System Wake - Full Wake/ Dark Wake / Maintenance wake
21/04/2016 02:00:01,000    kernel[0]    AirPort_Brcm43xx::checkInterfacePowerState: Check _pwrOffThreadCall!
21/04/2016 02:00:01,000    kernel[0]    Previous sleep cause: 5
21/04/2016 02:00:01,000    syslogd[43]    ASL Sender Statistics
21/04/2016 02:00:01,000    kernel[0]    00000000  00000020  NVEthernet::setLinkStatus - not Active
21/04/2016 02:00:03,000    kernel[0]    Ethernet [nvenet]: Link up on en0, 100-Megabit, Full-duplex, No flow-control, Debug [796d,0000,0de1,0005,41e1,0000]
21/04/2016 02:00:03,000    kernel[0]    05f5e100  00100026  NVEthernet::setLinkStatus - Active
21/04/2016 02:00:03,000    kernel[0]    in6_unlink_ifa: IPv6 address 0x7b5d5378fd3aba45 has no prefix
21/04/2016 02:00:03,151    configd[52]    LINKLOCAL en0: parent has no IP
21/04/2016 02:00:08,949    configd[52]    network changed: v4(en0-:192.168.0.11) DNS- Proxy-
21/04/2016 02:00:09,285    sandboxd[141]    ([413]) com.apple.WebKit(413) deny mach-lookup com.apple.dock.fullscreen
21/04/2016 02:00:09,528    com.apple.WebKit.WebContent[388]    [02:00:09.528] <<<< CRABS >>>> crabsFlumeHostUnavailable: [0x7fc422b2f5f0] Byte flume reports host unavailable.
21/04/2016 02:00:09,529    com.apple.WebKit.WebContent[388]    [02:00:09.529] <<<< CRABS >>>> crabsFlumeConnectionToHostLost: [0x7fc422b2f5f0] Byte flume reports connection to host lost. No error specified, using kCFURLErrorCannotConnectToHost.
21/04/2016 02:00:09,529    com.apple.WebKit.WebContent[945]    [02:00:09.529] <<<< CRABS >>>> crabsFlumeHostUnavailable: [0x7f8cb3b07340] Byte flume reports host unavailable.
21/04/2016 02:00:09,529    com.apple.WebKit.WebContent[945]    [02:00:09.529] <<<< CRABS >>>> crabsFlumeConnectionToHostLost: [0x7f8cb3b07340] Byte flume reports connection to host lost. No error specified, using kCFURLErrorCannotConnectToHost.
21/04/2016 02:00:09,553    symptomsd[199]    __73-[NetworkAnalyticsEngine observeValueForKeyPath:ofObject:change:context:]_block_invoke unexpected switch value 2
21/04/2016 02:00:09,591    netbiosd[816]    network_reachability_changed : network is not reachable, netbiosd is shutting down
21/04/2016 02:00:09,934    configd[52]    network changed: v4(en0+:192.168.0.11) DNS+ Proxy+ SMB
21/04/2016 02:00:10,447    symptomsd[199]    __73-[NetworkAnalyticsEngine observeValueForKeyPath:ofObject:change:context:]_block_invoke unexpected switch value 2
21/04/2016 02:00:10,513    SubmitDiagInfo[473]    Couldn't load config file from on-disk location. Falling back to default location. Reason: Won't serialize in _readDictionaryFromJSONData due to nil object
21/04/2016 02:00:21,062    sandboxd[141]    ([413]) com.apple.WebKit(413) deny mach-lookup com.apple.dock.fullscreen
21/04/2016 02:00:33,068    sandboxd[141]    ([413]) com.apple.WebKit(413) deny mach-lookup com.apple.dock.fullscreen
21/04/2016 02:00:45,073    sandboxd[141]    ([413]) com.apple.WebKit(413) deny mach-lookup com.apple.dock.fullscreen
21/04/2016 02:00:55,000    kernel[0]    PM response took 1994 ms (53, powerd)
21/04/2016 02:00:55,000    kernel[0]    AirPort_Brcm43xx:

owerChange: System Sleep 
21/04/2016 02:01:56,000    kernel[0]    00000000  00000020  NVEthernet::setLinkStatus - not Active
21/04/2016 02:00:56,000    kernel[0]    Wake reason: RTC (Alarm)