It looks like other sites (e.g., stack overflow) eventually shed the "got a question about the site itself?" hint box about the meta site.
It is a great hint for new users. So maybe it could stay forever, but go away automatically, after, you post your first Q or A in meta or reach a certain reputation level?
When a site is new and meta activity is low, top-of-mind awareness of meta isn't always important nor needed… until it is. So early on, it's simply too easy for meta to fall out of sight, out of mind until it become a useless ghost town… just as it is (potentially) needed the most.
That's why the system message is persistent through the private beta plus a few weeks more. But after that, it will be gone. We've been considering making these notifications dismissible, but under the current implementation, banners are designed to run for the duration of the notice.
