Guys this one has me stumped.
I get this on fresh start, on restart, on awakening from sleep and/or hibernation as best I can tell.
This is on a clean fresh install of Windows 8.1 Pro x64 on Dell Latitude E5440.
So far, for this particular gremlin I get Warnings, not "Critical" - Reading many posts on roughly similar BITS errors I seem to be lucky as some result in consistent BSOD's

I guess that the root cause is a device that is not coming into powered-up state in an interval BITS routine is looking for. It always occurs once or twice in quick succession when coming on, per above. At least its consistent

Log below:

General: BITS has encountered an error communicating with an Internet Gateway Device. Please check that the device is functioning properly. BITS will not attempt to use this device until the next system reboot. Error code: 0x80004005.

Log Name: System
Source: Microsoft-Windows-Bits-Client
Date: 3/1/2015 2:30:00 PM
Event ID: 16393
Task Category: None
Level: Warning
Keywords:
User: SYSTEM
Computer: Webster
Description:
BITS has encountered an error communicating with an Internet Gateway Device. Please check that the device is functioning properly. BITS will not attempt to use this device until the next system reboot. Error code: 0x80004005.
Event Xml:
<Event xmlns="http://schemas.microsoft.com/win/2004/08/events/event">
<System>
<Provider Name="Microsoft-Windows-Bits-Client" Guid="{EF1CC15B-46C1-414E-BB95-E76B077BD51E}" />
<EventID>16393</EventID>
<Version>0</Version>
<Level>3</Level>
<Task>0</Task>
<Opcode>0</Opcode>
<Keywords>0x8000000000000000</Keywords>
<TimeCreated SystemTime="2015-03-01T20:30:00.458861100Z" />
<EventRecordID>2879</EventRecordID>
<Correlation />
<Execution ProcessID="876" ThreadID="3772" />
<Channel>System</Channel>
<Computer>Webster</Computer>
<Security UserID="S-1-5-18" />
</System>
<EventData>
<Data Name="ErrorCode">2147500037</Data>
</EventData>
</Event>