I solved this issue by setting the time out to zero. Please see how I call the stored procedure from Azure Automation.
$DatabaseCommand = New-Object System.Data.SqlClient.SqlCommand
$DatabaseCommand.CommandType = [System.Data.CommandType]::StoredProcedure
$DatabaseCommand.Connection = $DatabaseConnection
# A value of 0 indicates no limit
$DatabaseCommand.CommandTimeout = 0
$DatabaseCommand.CommandText = $SP
Please update all modules if you are running the runbook from Azure Automation.
Try also to copy that data in batches as explained here. I suspect the DTU limit is reached and then throttling occurs creating the time outs.