You would be getting this message because the Inbox on the Suddenlink server is full. You may have cleared the Inbox in your mail client, but you need to reduce the number of messages on the Suddenlink server. Log into your Suddenlink email webmail account, and delete messages from the Inbox. You may want to consider changing the settings in your email client to delete the messages from the server after they are downloaded to your email client. Some options would be to set it to delete messages that you have read after 3 days, or as you delete them from your Inbox.
Email service is no longer available for new customers.