I had the same problem...
Found out it is because I use the two step verification process by Hotmail (which still doesn't deter someone from being able to hack your email).
Anyhow, the steps I took:
1) Go to your Hotmail account on your desktop computer
2) Under your name (top right corner), click on it and click on Account Settings
3) Click on Security and passwords (second option down on left hand pane)
4) Enter your password (if necessary)
5) Click on "Create a new app password" - half way down the screen
App passwords
Some apps and devices (such as Xbox 360, Windows Phone, or mail apps on your other devices) don't support security codes for two-step verification. In these cases, you need to create an app password to sign in. Learn more about app passwords.
Create a new app password
6) It will generate a password for you - enter this password in your iPhone as your Hotmail password
That is it. Alternatively, you can turn off the two step verification and it should use your regular password.
Hope that helps.