When you send emails through Kennel Connection, here is the process:
When you hit Send or it's time to send automatic emails, KC logs into your email provider's server. If your login information is authenticated, KC sends all the emails to your provider at once. That's all it does. It's now up to your email provider to send the emails to your client.
This error means your provider is rejecting this client's email as invalid. Verify the email address with your client. Make sure there are no spaces before or after the address. If it still fails, you will need to contact your email provider to find out why they are rejecting this email.