For what it's worth, after we turned off progress updates we haven't seen this bite us again, so that seems like a workable mitigation until the underlying issue is fixed.

We've been running into this issue regularly. We added the exception logging code that @rjmholt suggested above, which came back with this

ErrorRecord    : The pipeline was not run because a pipeline is already running. Pipelines cannot be run concurrently.
Message        : The pipeline was not run because a pipeline is already running. Pipelines cannot be run concurrently.
Data           : {}
InnerException : 
TargetSite     : Void DoConcurrentCheck(Boolean, System.Object, Boolean)
StackTrace     :    at System.Management.Automation.Runspaces.PipelineBase.DoConcurrentCheck(Boolean syncCall, Object 
                 syncObject, Boolean isInLock)
                    at System.Management.Automation.Runspaces.RunspaceBase.DoConcurrentCheckAndAddToRunningPipelines(Pi
                 pelineBase pipeline, Boolean syncCall)
                    at System.Management.Automation.Runspaces.PipelineBase.CoreInvoke(IEnumerable input, Boolean 
                 syncCall)
                    at System.Management.Automation.Runspaces.PipelineBase.Invoke(IEnumerable input)
                    at System.Management.Automation.PowerShell.Worker.ConstructPipelineAndDoWork(Runspace rs, Boolean 
                 performSyncInvoke)
                    at System.Management.Automation.PowerShell.Worker.CreateRunspaceIfNeededAndDoWork(Runspace 
                 rsToUse, Boolean isSync)
                    at System.Management.Automation.PowerShell.CoreInvokeHelper[TInput,TOutput](PSDataCollection`1 
                 input, PSDataCollection`1 output, PSInvocationSettings settings)
                    at System.Management.Automation.PowerShell.CoreInvoke[TInput,TOutput](PSDataCollection`1 input, 
                 PSDataCollection`1 output, PSInvocationSettings settings)
                    at System.Management.Automation.PowerShell.Invoke(IEnumerable input, PSInvocationSettings settings)
                    at Microsoft.Azure.Commands.Compute.Models.PSSyncOutputEvents.LogProgressComplete(Int32 
                 activityId, String activity)
                    at Microsoft.Azure.Commands.Compute.Models.PSSyncOutputEvents.ProgressUploadComplete(TimeSpan 
                 elapsed)
                    at Microsoft.WindowsAzure.Commands.Sync.ProgressTracker.Dispose(Boolean disposing)
                    at Microsoft.WindowsAzure.Commands.Sync.ProgressTracker.Dispose()
                    at Microsoft.WindowsAzure.Commands.Sync.Upload.BlobSynchronizer.Synchronize()
                    at Microsoft.Azure.Commands.Compute.Models.VhdUploaderModel.Upload(UploadParameters 
                 uploadParameters)
                    at Microsoft.Azure.Commands.Compute.StorageServices.AddAzureVhdCommand.ExecuteCmdlet()
                    at Microsoft.WindowsAzure.Commands.Utilities.Common.AzurePSCmdlet.ProcessRecord()
HelpLink       : 
Source         : System.Management.Automation
HResult        : -2146233079

In our case we're trying to run this as part of a CI system, and since this seems to be relating to the progress bar (which isn't even visible anywhere) we're going to see if we can set $ProgressPreference = "SilentlyContinue" to work around this for now.