A well automated system is a good key to being a large host, but the customer service has to remain human for them to survive or have a good reputation for the long term. If you automate your billing system and signup process you will sleep much more at night.
Agreed, an automated system is absolutely essential. If you end up experiencing rapid growth you would spend all your time on administrative tasks, when what you should be doing is working on your business!
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There is no need to check every hour; only when there is something that you need to take action on. Setup some simple scripts, options, forwards, whatever within your setup and you should be able to be notified of new accounts and new support tickets via SMS -- right to your cell phone.