This just started happening to me with my new 14" MBP. I use both an Exchange account and an iCloud account, and had previously used the default Mac Mail app to use them. Every time I open my computer, I get the Notification that I need to enter my password for Exchange Server. But when I click in, it never asks me for it (and when I open the Mail app, it doesn't either, and I can read / download e-mails as if the notification never happened).
Anyways, it was annoying enough that I've switched to using Outlook for my Exchange e-mail account.
Anyways, it was annoying enough that I've switched to using Outlook for my Exchange e-mail account.