I have a desktop PC that I mostly use as a document repository via a network share. And because that PC is usually unattended, it is highly unlikely that I will see a PMPC outdated app notification. By the way, I think the current 10 seconds is the right amount of time for the notification to display before it clears itself.
However, if the PMPC notifications were to persist in the Windows Notification Center that would be very helpful, because I wouldn't have to launch PMPC to see that there are outdated apps. Which after all is the objective of the notifications.