diff --git a/src/ModelContextProtocol/Protocol/Transport/SseResponseStreamTransport.cs b/src/ModelContextProtocol/Protocol/Transport/SseResponseStreamTransport.cs
index a89bd29c2..db96a53bb 100644
--- a/src/ModelContextProtocol/Protocol/Transport/SseResponseStreamTransport.cs
+++ b/src/ModelContextProtocol/Protocol/Transport/SseResponseStreamTransport.cs
@@ -20,7 +20,7 @@ public sealed class SseResponseStreamTransport(Stream sseResponseStream) : ITran
     private Utf8JsonWriter? _jsonWriter;
 
     /// <inheritdoc/>
-    public bool IsConnected => _sseWriteTask?.IsCompleted == false;
+    public bool IsConnected { get; private set; }
 
     /// <summary>
     /// Starts the transport and writes the JSON-RPC messages sent via <see cref="SendMessageAsync(IJsonRpcMessage, CancellationToken)"/>
@@ -41,6 +41,8 @@ void WriteJsonRpcMessageToBuffer(SseItem<IJsonRpcMessage?> item, IBufferWriter<b
             JsonSerializer.Serialize(GetUtf8JsonWriter(writer), item.Data, McpJsonUtilities.DefaultOptions.GetTypeInfo<IJsonRpcMessage?>());
         }
 
+        IsConnected = true;
+
         // The very first SSE event isn't really an IJsonRpcMessage, but there's no API to write a single item of a different type,
         // so we fib and special-case the "endpoint" event type in the formatter.
         _outgoingSseChannel.Writer.TryWrite(new SseItem<IJsonRpcMessage?>(null, "endpoint"));
@@ -55,6 +57,7 @@ void WriteJsonRpcMessageToBuffer(SseItem<IJsonRpcMessage?> item, IBufferWriter<b
     /// <inheritdoc/>
     public ValueTask DisposeAsync()
     {
+        IsConnected = false;
         _incomingChannel.Writer.TryComplete();
         _outgoingSseChannel.Writer.TryComplete();
         return new ValueTask(_sseWriteTask ?? Task.CompletedTask);
@@ -63,7 +66,7 @@ public ValueTask DisposeAsync()
     /// <inheritdoc/>
     public async Task SendMessageAsync(IJsonRpcMessage message, CancellationToken cancellationToken = default)
     {
-        if (_sseWriteTask is null)
+        if (!IsConnected)
         {
             throw new InvalidOperationException($"Transport is not connected. Make sure to call {nameof(RunAsync)} first.");
         }
@@ -80,7 +83,7 @@ public async Task SendMessageAsync(IJsonRpcMessage message, CancellationToken ca
     /// <exception cref="InvalidOperationException">Thrown when there is an attempt to process a message before calling <see cref="RunAsync(CancellationToken)"/>.</exception>
     public async Task OnMessageReceivedAsync(IJsonRpcMessage message, CancellationToken cancellationToken)
     {
-        if (_sseWriteTask is null)
+        if (!IsConnected)
         {
             throw new InvalidOperationException($"Transport is not connected. Make sure to call {nameof(RunAsync)} first.");
         }