DNS can be the cause of the issues. You can misconfigure the server, you can misconfigure NS glue, your registration can lapse, etc. If you have a second domain for your status page, it's less likely that a DNS problem with your primary domain will make that unavailable.

There is a tradeoff, of course. Your automated configuration management system can dutifully push the misconfiguration to both domains. You might not ever configure the second domain correctly, because it's not like customers are visiting and reporting back "hey your status page is broken".

In my mind, I'm not sure how useful this is in practice, however. I would never think to look for status updates at anything other than status.myapp.com. I'm not sure I'd make the leap to myappstatus.com, and I'm not sure it's going to rank particularly high in search engines. I'd probably look at Twitter second. (I'm not even sure if people routinely check status pages. If you visited my personal website, jrock.us, and it didn't load, would you check status.jrock.us? That actually exists, but I bet that nobody has ever visited it.)

Suppose the outage was caused by an issue with the registrar, DNS, the name server, or the domain registration itself. Having a separate domain for the status page — ideally purchased through a different provider – could prevent a lot of issues.