Did you follow the below steps?
1. Go to Settings-Mail, Contact, Calendars
2. Tap on the email account you're trying to delete.
3.Scroll to the bottom and tap on "Delete Account".
If you did that, and then tried again using the above instructions, but was still unable to delete the account, check the restrictions setting, if enabled.
Settings-General-Restrictions-Accounts and then select "Allow Changes".
Oh okay. Hmmm, try logging on to the website via mobile Safari and see if you can delete it or move it to the trash bin. A quick look at their Status Page reveals that everything should be working properly.
https://status.live.com