diff --git a/src/Microsoft.AspNetCore.SpaServices/Webpack/ConditionalProxyMiddleware.cs b/src/Microsoft.AspNetCore.SpaServices/Webpack/ConditionalProxyMiddleware.cs
index 5a56c81..72b66c3 100644
--- a/src/Microsoft.AspNetCore.SpaServices/Webpack/ConditionalProxyMiddleware.cs
+++ b/src/Microsoft.AspNetCore.SpaServices/Webpack/ConditionalProxyMiddleware.cs
@@ -30,7 +30,6 @@ namespace Microsoft.AspNetCore.SpaServices.Webpack
             _pathPrefix = pathPrefix;
             _options = options;
             _httpClient = new HttpClient(new HttpClientHandler());
-            _httpClient.Timeout = _options.RequestTimeout;
         }
 
         public async Task Invoke(HttpContext context)
diff --git a/src/Microsoft.AspNetCore.SpaServices/Webpack/ConditionalProxyMiddlewareOptions.cs b/src/Microsoft.AspNetCore.SpaServices/Webpack/ConditionalProxyMiddlewareOptions.cs
index 2c3311a..5654007 100644
--- a/src/Microsoft.AspNetCore.SpaServices/Webpack/ConditionalProxyMiddlewareOptions.cs
+++ b/src/Microsoft.AspNetCore.SpaServices/Webpack/ConditionalProxyMiddlewareOptions.cs
@@ -1,20 +1,16 @@
-using System;
-
 namespace Microsoft.AspNetCore.SpaServices.Webpack
 {
     internal class ConditionalProxyMiddlewareOptions
     {
-        public ConditionalProxyMiddlewareOptions(string scheme, string host, string port, TimeSpan requestTimeout)
+        public ConditionalProxyMiddlewareOptions(string scheme, string host, string port)
         {
             Scheme = scheme;
             Host = host;
             Port = port;
-            RequestTimeout = requestTimeout;
         }
 
         public string Scheme { get; }
         public string Host { get; }
         public string Port { get; }
-        public TimeSpan RequestTimeout { get; }
     }
 }
\ No newline at end of file
diff --git a/src/Microsoft.AspNetCore.SpaServices/Webpack/WebpackDevMiddleware.cs b/src/Microsoft.AspNetCore.SpaServices/Webpack/WebpackDevMiddleware.cs
index d046c28..dcc5d4f 100644
--- a/src/Microsoft.AspNetCore.SpaServices/Webpack/WebpackDevMiddleware.cs
+++ b/src/Microsoft.AspNetCore.SpaServices/Webpack/WebpackDevMiddleware.cs
@@ -7,7 +7,6 @@ using Microsoft.AspNetCore.Builder;
 using Microsoft.AspNetCore.Hosting;
 using Microsoft.Extensions.PlatformAbstractions;
 using Newtonsoft.Json;
-using System.Threading;
 
 // Putting in this namespace so it's always available whenever MapRoute is
 
@@ -15,6 +14,8 @@ namespace Microsoft.AspNetCore.Builder
 {
     public static class WebpackDevMiddleware
     {
+        private const string WebpackDevMiddlewareScheme = "http";
+        private const string WebpackHotMiddlewareEndpoint = "/__webpack_hmr";
         private const string DefaultConfigFile = "webpack.config.js";
 
         public static void UseWebpackDevMiddleware(
@@ -61,27 +62,30 @@ namespace Microsoft.AspNetCore.Builder
                     JsonConvert.SerializeObject(devServerOptions)).Result;
 
             // Proxy the corresponding requests through ASP.NET and into the Node listener
-            // Anything under /<publicpath> (e.g., /dist) is proxied as a normal HTTP request with a typical timeout (100s is the default from HttpClient),
-            // plus /__webpack_hmr is proxied with infinite timeout, because it's an EventSource (long-lived request).
-            appBuilder.UseProxyToLocalWebpackDevMiddleware(devServerInfo.PublicPath, devServerInfo.Port, TimeSpan.FromSeconds(100));
-            appBuilder.UseProxyToLocalWebpackDevMiddleware("/__webpack_hmr", devServerInfo.Port, Timeout.InfiniteTimeSpan);
-        }
-
-        private static void UseProxyToLocalWebpackDevMiddleware(this IApplicationBuilder appBuilder, string publicPath, int proxyToPort, TimeSpan requestTimeout)
-        {
             // Note that this is hardcoded to make requests to "localhost" regardless of the hostname of the
             // server as far as the client is concerned. This is because ConditionalProxyMiddlewareOptions is
             // the one making the internal HTTP requests, and it's going to be to some port on this machine
             // because aspnet-webpack hosts the dev server there. We can't use the hostname that the client
             // sees, because that could be anything (e.g., some upstream load balancer) and we might not be
             // able to make outbound requests to it from here.
-            // Also note that the webpack HMR service always uses HTTP, even if your app server uses HTTPS,
-            // because the HMR service has no need for HTTPS (the client doesn't see it directly - all traffic
-            // to it is proxied), and the HMR service couldn't use HTTPS anyway (in general it wouldn't have
-            // the necessary certificate).
-            var proxyOptions = new ConditionalProxyMiddlewareOptions(
-                "http", "localhost", proxyToPort.ToString(), requestTimeout);
-            appBuilder.UseMiddleware<ConditionalProxyMiddleware>(publicPath, proxyOptions);
+            var proxyOptions = new ConditionalProxyMiddlewareOptions(WebpackDevMiddlewareScheme,
+                "localhost", devServerInfo.Port.ToString());
+            appBuilder.UseMiddleware<ConditionalProxyMiddleware>(devServerInfo.PublicPath, proxyOptions);
+
+            // While it would be nice to proxy the /__webpack_hmr requests too, these return an EventStream,
+            // and the Microsoft.AspNetCore.Proxy code doesn't handle that entirely - it throws an exception after
+            // a while. So, just serve a 302 for those. But note that we must use the hostname that the client
+            // sees, not "localhost", so that it works even when you're not running on localhost (e.g., Docker).
+            appBuilder.Map(WebpackHotMiddlewareEndpoint, builder =>
+            {
+                builder.Use(next => ctx =>
+                {
+                    var hostname = ctx.Request.Host.Host;
+                    ctx.Response.Redirect(
+                        $"{WebpackDevMiddlewareScheme}://{hostname}:{devServerInfo.Port.ToString()}{WebpackHotMiddlewareEndpoint}");
+                    return Task.FromResult(0);
+                });
+            });
         }
 
 #pragma warning disable CS0649