So, maybe you've run into this bug: you get a notification for your Elites tab -- maybe it's a new doctrine, a Mastery skin, or something similar -- and you click, see the icon on the faction in question, follow the breadcrumbs, and clear the notification... except on the Elites tab.
You've checked everywhere, there's nothing new, but the game won't clear the notification!
Maybe you don't care. But if you're in this thread, I'm guessing you do: personally, I can't stand to have notifications showing in error -- one of my biggest pet peeves (i.e. not of the greater issues) when it came to Mass Effect Andromeda was the persistent (!) showing in error, but I digress.
Today while troubleshooting other issues, I discovered that the "wipe and reset" option of clearing your My Documents \ My Games \ Dawn of War 3 \ folders + an uninstall / reinstall +will+ fix the persistent Elites notifier. Now it'll properly show clear, and you'll only see it pop back up when you unlock something new.
That said, I don't know that it won't happen again; if it does, I'll try to see if the folder wipe without reinstall fixes it, and report back.
Happy hunting, fellow wayfarers!