SSAS Cube processing randomly fails with 08S01 error

We have a cube which is scheduled to process every morning at 6:00 to run at SSAS 10.50.2500.0.

Sometimes it does it ok. More often than not, it fails.

When it happens, SQL Server has this entry in the log (XML beautified):

[136] Job OLAP_Refresh reported: 
<return xmlns="urn:schemas-microsoft-com:xml-analysis">
    <results xmlns="http://schemas.microsoft.com/analysisservices/2003/xmla-multipleresults">
        <root xmlns="urn:schemas-microsoft-com:xml-analysis:empty">
            <Exception xmlns="urn:schemas-microsoft-com:xml-analysis:exception" />
            <Messages xmlns="urn:schemas-microsoft-com:xml-analysis:exception">
                <Error ErrorCode="3238395904" Description="OLE DB error: OLE DB or ODBC error: Communication link failure; 08S01; TCP Provider: The specified network name is no longer available.&#xA;; 08S01." Source="Microsoft SQL Server 2008 R2 Analysis Services" HelpFile="" />
                <Error ErrorCode="3240034318" Description="Errors in the OLAP storage engine: An error occurred while processing the '__PARTITION__' partition of the '__MEASURE_GROUP__' measure group for the '__CUBE__' cube from the __OLAP__ database." Source="Microsoft SQL Server 2008 R2 Analysis Services" HelpFile="" />
                <Error ErrorCode="3238002695" Description="Internal error: The operation terminated unsuccessfully." Source="Microsoft SQL Server 2008 R2 Analysis Services" HelpFile="" />
                <Error ErrorCode="3239837698" Description="Server: The operation has been cancelled." Source="Microsoft SQL Server 2008 R2 Analysis Services" HelpFile="" />
            </Messages>
        </root>
    </results>
</return>

Where __PARTITION__ and __MEASURE_GROUP__ are not always the same and once in awhile job finishes without a problem.

msmdsrv.log has entries like this:

($DATE $TIME) Message: OLE DB error: OLE DB or ODBC error: Communication link failure; 08S01; TCP Provider: The specified network name is no longer available.
; 08S01. (Source: \\?\P:\Microsoft SQL Server\MSSQL.2\OLAP\Log\msmdsrv.log, Type: 3, Category: 289, Event ID: 0xC1210003)
($DATE $TIME) Message: OLE DB error: OLE DB or ODBC error: Protocol error in TDS stream; HY000; Communication link failure; 08S01; TCP Provider: An established connection was aborted by the software in your host machine.
; 08S01; Communication link failure; 08S01; TCP Provider: An established connection was aborted by the software in your host machine.
; 08S01; Communication link failure; 08S01; TCP Provider: An established connection was aborted by the software in your host machine.
; 08S01. (Source: \\?\P:\Microsoft SQL Server\MSSQL.2\OLAP\Log\msmdsrv.log, Type: 3, Category: 289, Event ID: 0xC1210003)

Data center swears that there are no network issues.

$TIME is usually around 6:40, though today it failed around 8:40.

ExternalCommandTimeout is set to 50000.

Update doesn't run in parallel, here's what job sends every morning:

<Batch xmlns="http://schemas.microsoft.com/analysisservices/2003/engine">
  <ErrorConfiguration xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ddl2="http://schemas.microsoft.com/analysisservices/2003/engine/2" xmlns:ddl2_2="http://schemas.microsoft.com/analysisservices/2003/engine/2/2" xmlns:ddl100_100="http://schemas.microsoft.com/analysisservices/2008/engine/100/100" xmlns:ddl200="http://schemas.microsoft.com/analysisservices/2010/engine/200" xmlns:ddl200_200="http://schemas.microsoft.com/analysisservices/2010/engine/200/200">
    <KeyNotFound>IgnoreError</KeyNotFound>
    <NullKeyNotAllowed>IgnoreError</NullKeyNotAllowed>
  </ErrorConfiguration>
  <Process xmlns:xsd="http://www.w3.org/2001/XMLSchema" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:ddl2="http://schemas.microsoft.com/analysisservices/2003/engine/2" xmlns:ddl2_2="http://schemas.microsoft.com/analysisservices/2003/engine/2/2" xmlns:ddl100_100="http://schemas.microsoft.com/analysisservices/2008/engine/100/100" xmlns:ddl200="http://schemas.microsoft.com/analysisservices/2010/engine/200" xmlns:ddl200_200="http://schemas.microsoft.com/analysisservices/2010/engine/200/200">
    <Object>
      <DatabaseID>__OLAP__</DatabaseID>
    </Object>
    <Type>ProcessFull</Type>
    <WriteBackTableCreation>UseExisting</WriteBackTableCreation>
  </Process>
</Batch>'

Executing the job manually works more reliably (I started it three times and it failed once with the same errors), though it might be because I start it around 10:00-14:00

Any idea what it can be and how to fix this?