How to troubleshoot random error while sending email from ASP.NET website

I send emails from ASP.NET (4.0) website:

SmtpClient mySMTPClient = new SmtpClient();
mySMTPClient.UseDefaultCredentials = false;
mySMTPClient.Host = "email.privateemail.com";
mySMTPClient.Port = 465; //I also tried 587 and none of them
mySMTPClient.Credentials = new System.Net.NetworkCredential("contact@xxxxxx.com", "xxxxxxxxxx");
mySMTPClient.EnableSsl = true;
mySMTPClient.DeliveryMethod = SmtpDeliveryMethod.Network;
mySMTPClient.Send(email);

I send a dozen of emails / day and not in batch or in loop. Only about half of them are sent. The other fail with error:

ERROR MESSAGE: Failure sending mail.
INNER EXCEPTION: System.IO.IOException: Unable to read data from the transport connection: An existing connection was forcibly closed by the remote host. ---> System.Net.Sockets.SocketException: An existing connection was forcibly closed by the remote host
   at System.Net.Sockets.Socket.Receive(Byte[] buffer, Int32 offset, Int32 size, SocketFlags socketFlags)
   at System.Net.Sockets.NetworkStream.Read(Byte[] buffer, Int32 offset, Int32 size)
   --- End of inner exception stack trace ---
   at System.Net.Sockets.NetworkStream.Read(Byte[] buffer, Int32 offset, Int32 size)
   at System.Net.DelegatedStream.Read(Byte[] buffer, Int32 offset, Int32 count)
   at System.Net.BufferedReadStream.Read(Byte[] buffer, Int32 offset, Int32 count)
   at System.Net.Mail.SmtpReplyReaderFactory.ReadLines(SmtpReplyReader caller, Boolean oneLine)
   at System.Net.Mail.SmtpReplyReaderFactory.ReadLine(SmtpReplyReader caller)
   at System.Net.Mail.SmtpConnection.GetConnection(ServicePoint servicePoint)
   at System.Net.Mail.SmtpTransport.GetConnection(ServicePoint servicePoint)
   at System.Net.Mail.SmtpClient.GetConnection()
   at System.Net.Mail.SmtpClient.Send(MailMessage message)

The failing emails are random. I don't have a pattern.

Windows server 2008 SP2 build 6002 Firewall PfSense - engineer says rules are configured properly, otherwise all emails would fail. 3rd part email provider: they say everything is configured properly with them and they cannot make any modification on their side anyways.

I am not a network engineer and I don't have one. My question is, what do I do to find the root cause so I can address it?

By now I tried Process Monitor but it doesn't help me (or I don't know how to look).

I found several articles on this problem, none help me by now as their solutions don't apply to my context (I tried some with no success).

Thank you