What is reasonable downtime?

As someone who deals all day long with projects that seem to have some kind of death wish, I tend to be pretty patient and understanding when it comes to periodic downtime and crashes. The folks I work for are somewhat the opposite. Sites go down for more than two or three attempts to refresh and my phone is ringing or they're in my space. I always say "give it five minutes and it'll probably be back". If it goes beyond that, I say "give it five more", but by then they're already starting to freak out and looking at me like I'm supposed to do something.

So, how long is it reasonable to wait before going the support route?

Also, behind the scenes, are the people running the servers almost always aware of a regular problem? Like, is there a screen or a panel that lights up and says "server X is freaking out"? I always assume that if the server just isn't coming up, it will be back in five or 10 minutes because someone is probably already working on it. Am I right, or should I share my company's sense of hyper urgency? (We aren't dealing with a bank or weapon's system.)

1) When you observe an issue that is server related, immediately file a support ticket. It's easier to close a ticket IMO than wait for someone to notice a problem.
2) There is no SLA with Dreamhost, at least none that I can find in the Terms of Service. Thus, "reasonable" is a judgement call, since it isn't defined.
3) I don't know what DreamHost uses to keep an eye on their servers. There are products out there (some opensource, some paid-for) that keep an eye on your server for you with defined checks. Nagios is a big one, and I use it at my place of employment. You can keep an eye on just about anything under the sun with Nagios, it's quite an awesome package.

So, I don't think a shared hosting package is really the route to go if your client or employer demands a certain level of uptime. If there's an SLA that DreamHost offers, I haven't found it, and you NEED one if your site is required to be highly available.