Getting SocketException while calling BeginSend

Question

I need to write an app that accepts incoming sockect connections and sends some data to all off them every N ms. My code:

private readonly Timer _senderTimer;
private readonly Socket _serverSocket = new Socket(AddressFamily.InterNetwork, SocketType.Stream, ProtocolType.Tcp);
private readonly ConcurrentDictionary<EndPoint, Socket> _clientConnections =
            new ConcurrentDictionary<EndPoint, Socket>();

public Start(SettingsProvider settingsProvider)
{
    _senderTimer = new Timer(SendIntervalTick, null, settingsProvider.SendInterval, Timeout.Infinite);
    _serverSocket.Bind(new IPEndPoint(selfIp, selfPort));
    _serverSocket.Listen(MaxLengthOfPendingConnectionsQueue);
    _serverSocket.BeginAccept(AcceptCallback, null);
}

private void AcceptCallback(IAsyncResult result)
{
    EndPoint endPoint = null;
    try
    {
        var acceptedSocket = _serverSocket.EndAccept(result);
        endPoint = acceptedSocket.RemoteEndPoint;
        _clientConnections.TryAdd(endPoint, acceptedSocket);
    }
    catch (Exception e)
    {
        CloseSocket(endPoint);
    }
    finally
    {
        _serverSocket.BeginAccept(AcceptCallback, null);
    }
}

private void SendIntervalTick(object state)
{
    SendPacket(new[] {(byte)0xFF});
    _senderTimer.Change(Math.Max(0, _sendInterval - watch.ElapsedMilliseconds), Timeout.Infinite);
}

private void SendPacket(byte[] packet)
{
    var connToRemove = new List<EndPoint>();
    var connToSend = _clientConnections.ToDictionary(x => x.Key, x => x.Value);
    // Send packet to all connected clients
    foreach (var connection in connToSend)
    {
        try
        {
            connection.Value.BeginSend(packet, 0, packet.Length, 
                SocketFlags.None, 
                SendCallback, 
                new ClientConnection(connection.Key, connection.Value));
        }
        catch (Exception e)
        {
            // Get System.Net.Sockets.SocketException (0x80004005): An established connection was aborted by the software in your host machine here!!!
            connToRemove.Add(connection.Key);
        }
    }
    // Close broken connections
    foreach (var endPoint in connToRemove)
    {
        CloseSocket(endPoint);
    }
}

private void SendCallback(IAsyncResult result)
{
    var connection = (ClientConnection)result.AsyncState;
    try
    {
        connection.Sock.EndSend(result);
    }
    catch (Exception e)
    {
        CloseSocket(connection.RemoteEndPoint);
    }
}

private void CloseSocket(EndPoint endPoint)
{
    Socket socketToClose;
    _clientConnections.TryGetValue(endPoint, out socketToClose)
    try
    {
        socketToClose.Close();
        socketToClose.Dispose();
    }
    catch (Exception e)
    {
        Logger.Error("Error of closing/disposing socket.", e);
    }
    finally
    {
        Socket removable;
        if (!_clientConnections.TryRemove(endPoint, out removable))
        {
            Logger.Warn("Can not remove an endPoint ({0}) from the client-connections-dict ({1}).",
                endPoint, string.Join(", ", _clientConnections.Keys));
        }
    }
}

Now I get an exception

System.Net.Sockets.SocketException (0x80004005): An established connection was aborted by the software in your host machine

when call BeginSend among 20-50 successful sent. What I've noticed is that exception always throws soon after new connection accepted:

TRACE 674 bytes successfully sent to client 212.193.xxx.xxx:21666
TRACE 674 bytes successfully sent to client 212.193.xxx.xxx:21666
DEBUG An endPoint (212.193.xxx.xxx:22014) successfully added to the client-connections-dict (212.193.xxx.xxx:21666, 212.193.xxx.xxx:22014) 
TRACE 674 bytes successfully sent to client 212.193.xxx.xxx:21666 
TRACE 674 bytes successfully sent to client 212.193.xxx.xxx:22014 
WARN Closing socket 212.193.xxx.xxx:21666 because of exception while BeginSend: System.Net.Sockets.SocketException (0x80004005): An established connection was aborted by the software in your host machine

But I don't know why the error occurs and how to fix it. Please help!

EDIT: I've sniffed the traffic and found out that one of clients (who always was a source of problems) periodically sends tcp packet with a Reset flag. That's why I failed to send packet to it. According to this answer this may may occure because of server received packet for a closed socket. I wonder why this may happen and how server should behave in this situation.