I smell peoplebot.
That sounds like server or end-user trouble. Can't blame the Support guys
Support allow 24 hours "response time". Assuming the problem wasn't caused by the end-user themselves and is an actual DreamHost issue then the "resolution" is made (read: they fix the problem) before responding to the ticket. If it isn't fixed in 24 hours then we get an auto-response. Tickets are removed from the queue once a problem is resolved, which is sensible.
It is never impossible for account holders to get in touch with Support.
I'm not entirely sure what you're on about there mate.
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