When a customer is not getting the attention it demands it will find it ways to get it. He could call the manager of the Support Center if he knows his name (or number). But often your CEO is called directly. Especially large companies operate this way. Your CEO is not waiting for such frustrating calls. He will delegate immediately.
Having a group installed handling Customer Escalations provides the option to quickly redirect Escalating Customers. The Escalation manager is the contact person for the customer. He should organize calls with the customer to inform the customer about progress. When customers are at the top of their escalation daily calls are no exception. When the escalation goes to an end a call on a weekly basis is often enough.When the escalation has ended the customer need to return to normal Support and Maintenance mode. The customer and the rest of your organization should be informed about it. Internally an escalation list could help you providing this information but a personal call or email will do a much better job.