File download from azure services hosted application get stuck for IE 11 - asp.net-mvc

Question

We noticed that file download get stuck after some time in IE 11 client browser if downloaded from ASP.NET MVC application deployed to Azure service. The file download starts normally in IE 11. For several minutes the downloaded file size get increased. Then the yet downloaded file size get stuck with no more increases. If we continue to wait even more for around 1h, then the IE shows 'download was interrupted' error.
Azure instances have IIS 8.5 on board with app pool in default integrated pipeline mode. Application is ASP.NET MVC 5, targeted .NET 4.5.2.
There are no problems with download from Azure for Chrome browser.
There are no problems with download from local IIS express for both IE 11 and Chrome browsers.
There are no problems with download from local IIS 7.5 for both IE 11 and Chrome browsers.
So it looks like the only problem pair is Azure hosted IIS 8.5 + IE 11.
Application use the following code to stream file to client:
private const int StreamBufferSize = 1024*128; // 128KB
public static async Task StreamData(string fileName, Func<Stream, Task> streamFiller, HttpResponseBase response)
{
response.AddHeader("Content-Disposition", string.Format("attachment;filename=\"{0}\"", fileName));
response.ContentType = MimeMapping.GetMimeMapping(fileName);
response.BufferOutput = false;
using (Stream outputStream = new BufferedStream(response.OutputStream, StreamBufferSize))
{
await streamFiller(outputStream);
}
}
Where 'streamFiller()' is externally passed Func that writes data to the stream.
Please note that file is not so large, around 20Mb, but server do not send it at once. Instead server streams file with buffered chunks (see code above). Time between each chunk get streamed (buffer flashed) may be as long as several minutes.
By looking into Azure IIS I found that the client request looks like the following:
during normal download phase: State: ExecureRequestHandler, Module Name: ManagedPipelineHandler
since the download get stuck: State: SendResponse, Module Name: RemoveUnnecessaryHeadersModule.
To be clear what is RemoveUnnecessaryHeadersModule: we do the 'Server' header removing as following:
public class RemoveUnnecessaryHeadersModule : IHttpModule
{
public void Init(HttpApplication context)
{
// This only works if running in IIS7+ Integrated Pipeline mode
if (!HttpRuntime.UsingIntegratedPipeline) return;
context.PreSendRequestHeaders += (sender, e) =>
{
var app = sender as HttpApplication;
if (app != null && app.Context != null)
{
app.Context.Response.Headers.Remove("Server");
}
};
}
}