I noticed a problem with hotmail on my wife's PC yesterday and did some investigation. It appears there were some security changes at the site over the past few days and hotmail has invalidated the login and asking for additional security information. I'm not sure what the reason is or who was affected but one of the symptoms is exactly what you described.
To verify open a browser window in safari and go to Sign In and attempt to login. If you get prompted for additional login information then you've identified the problem. You'll need to change your password and then go into mail and make the changes there.
I hope Wpeace's info has solved your issue, let us know how you went.
The IPad Forum is a community of members from all walks of life and from all over the world coming together to share our experiences and to help each other learn about this wonderful piece of technology the Ipad. There is a wealth of information already here in the many threads we have so doing some searches will answer most of the questions you have. If then you cannot find the answer you are seeking then by all means post your question. There are many friendly and informed members here only too willing to help you.