After researching various hosts, I still get the feeling that it is somewhat impossible to get a host that would never go down.
Maybe these hosts employ redundancy, maybe they do not. Either case, how would one display a friendly message to the user along the lines of “BRB”. What if your host goes down completely for an hour? You would need a way to tell users you would be back. How do you accomplish that?
I doubt any ISP or hosting provider would do that for you. To archieve that you need very expensive and complicated infrastructure like redundant fail-safe routers and backbones in addition to servers of course – and you need multiple. The concepts like Simple Failover requires DNS updates which take minutes to hours to propagate normally, so it’s not a 100% solution either. See a good Joel’s article for a related discussion.