Gina, will you clarify the behavior please? Did you click on the notifications themselves (ie the text "2 accepted...") or the Notifications button on the grey bar? The way BP works, as I understand it, is that clicking the Notifications button will NOT, and is not really supposed to, made the new notifications message go away. You have to click the notifications themselves, ie the text that drops down when you hover over the Notifications button.
I'm about to send you a friendship request so you'll have a notification to test with.
If what I've written accurately describes your experience, then it's not a bug, it's a feature! An annoying feature. I will work on a patch that makes notifications go away once they've been viewed, like Facebook works.
If the notifications are there even after clicking on the text itself, then we may have a real bug on our hands. I was unable to reproduce it, though.