I suppose you are using the new calendar app for your appointments, right?
While the calendar app is great, it's only a preview app and it's possible they will add a tray notification in Windows 8 RC
If you want to minimize your appointments and "forget about them" and get a message when they are due your best bet is probably
Swift To Do List
You can add "reminders" before due date and then you will get notified even when the program is not opened