Delayed or no New Mail Notifications for Outlook 2013 on Windows 8

I’m using Outlook 2013 on Windows 8 and lately I’ve begun to notice that I don’t get any New Mail Notifications or that I get a notification long after I’ve already noticed that I received a message.

The emails are delivered to my Inbox and as far as I can tell, I have all the New Mail Notification options enabled in Outlook.

How can I get the Notifications as soon as new emails are being received?