Welcome to SO. From what I can infer from your description your are not handling the exception that is thrown by SendMessage.
Handle the exception in the caller method. Or do a dirty fix as shown below...
This is not a real fix. But will help you understand the issue...You have to determine in your calling method what to do if SendMessage throws an exception.
public static void SendMessage(String sender, String recipient, String message, String object)
{
try
{
MailMessage mail = new MailMessage(sender, recipient);
mail.Subject = object;
mail.IsBodyHtml = true;
mail.Body = message;
SmtpClient smtp = new SmtpClient();
smtp.Host = "my.smtp.com";
smtp.Send(mail);
}
catch (Exception e)
{
//Just log error and continue to process
}
}