If you are not ready to upgrade to 1.2.11, you can always explore this option.

1_Log4NetCustomSmtpAppender.cs

/// <summary>
/// This is a custom appender so that we can set enable SSL properly (and support TLS)
/// </summary>
public class SmtpCustomAppender : SmtpAppender
{
  public bool EnableSsl { get; set; }

  public SmtpCustomAppender()
  {
      Authentication = SmtpAuthentication.None;
      Port = 25; //0x19;
      //Port = 587; // 0x24b;
      Priority = MailPriority.Normal;
      EnableSsl = false;
  }

  /// <summary>
  /// Send the email message - this overrides the email sender so that we can add enabling SSL
  /// </summary>
  /// <param name="messageBody">the body text to include in the mail</param>
  protected override void SendEmail(string messageBody)
  {
      SmtpClient client = new SmtpClient();
      if (!string.IsNullOrEmpty(SmtpHost))
      {
          client.Host = SmtpHost;
      }
      client.Port = Port;
      client.EnableSsl = EnableSsl;
      client.DeliveryMethod = SmtpDeliveryMethod.Network;
      switch (Authentication)
      {
          case SmtpAuthentication.Basic:
              client.Credentials = new NetworkCredential(Username, Password);
              break;
          case SmtpAuthentication.Ntlm:
              client.Credentials = CredentialCache.DefaultNetworkCredentials;
              break;
      }

      MailMessage message = new MailMessage
          {
              Body = messageBody,
              From = new MailAddress(From)
          };
      message.To.Add(To);
      message.Subject = Subject;
      message.Priority = Priority;
      client.Send(message);
  }
}

2_log4net.config

<appender name="ErrorSmtpAppender" type="SomeProject.Infrastructure.Logging.Log4netAppenders.SmtpCustomAppender">
  <authentication value="Basic" />
  <smtpHost value="mail.gmail.com" />
  <username value="[email protected]" />
  <password value="somepassword" />
  <enablessl value="true" />
  <port value="587" />
  <to value="some folks" />
  <from value="[email protected]" />
  <subject value="Some subject - Environment" />
  <bufferSize value="2" />
  <lossy value="true" />
  <evaluator type="log4net.Core.LevelEvaluator">
    <threshold value="ERROR" />
  </evaluator>
  <layout type="log4net.Layout.PatternLayout">
    <conversionPattern value="%newline%date [%thread] %-5level %logger - %message%newline" />
    <!--<conversionPattern value="%newline%date [%thread] %-5level %logger [%property{NDC}] - %message%newline" />-->
  </layout>
</appender>