explicitly set the KeepAlive property to FALSE

namespace YourNamespace
{
    using System.Diagnostics;
    using System.Web.Services;
    using System.ComponentModel;
    using System.Web.Services.Protocols;
    using System;
    using System.Xml.Serialization;
    /// <summary>
    /// This partial class makes it so all requests specify
    /// "Connection: Close" instead of "Connection: KeepAlive" in the HTTP headers.
    /// </summary>
    public partial class YourServiceNameWse : Microsoft.Web.Services3.WebServicesClientProtocol
    {
        protected override System.Net.WebRequest GetWebRequest(Uri uri)
        {
            System.Net.HttpWebRequest webRequest = (System.Net.HttpWebRequest)base.GetWebRequest(uri);
            webRequest.KeepAlive = false;
            return webRequest;
        }
    }
}