I'm having the same problem. This isn't the "changing your main account" problem discussed on WPCentral's main page, but something with secondary email addresses. My main Windows Live account has my gmail account as its name; that is unchanged. However, I also have a secondary account that I use for certain stuff. It used to be @live.com; I just changed it to @outlook.com.
The calendar appointments I have with the @outlook.com account are still showing up on my calendar, but it didn't create a mail tile for my @outlook.com account. When I had originally linked this second account, a mail tile just appeared at the bottom for it.
Any ideas?
EDIT: problem solved. Go into "email and accounts," select your @outlook.com address and make sure that email is checked to sync. For me, it was off whereas the rest was on, for some reason.