Perhaps add a mouseover for the X button below.
“Click to close this site notice. Don’t worry. You can always see previous site notices again by looking in …”
(No, please don’t say “You can see previous site notices by looking in Job Listings”, because not all site notices are job listings. There needs to be a more general storage place the user can access previously dismissed site notices. Not just for Meta either. But for any site’s Discourse that hasn’t deleted them.)