Here is the process for sending emails through Kennel Connection:
When you hit Send or it's time to send automatic emails, KC logs into your email provider's server. Once your login information has been authenticated, KC sends all emails to your provider at once. That's all it does. It is up to your provider to send the emails to your clients.
This error means that at some point during the transmission of the email, an error is occurring on the provider's SMTP server and is not accepting the connection or user ID/password. This is all we can tell from this error. You will need to give your provider the error and have them look into why this is happening.