We have this issue on all of our iPads connecting into Exchange everytime somebody changes their Active Directory password.
Idealy the user should change their Exchange Password from in Settings, Mail Contacts and calendars.......etc.. as soon as they have changed their password.
If you do get to the point where you are promoted to put your password in but it doesn't work, just keep cancelling the message until it goes away (it will eventually) then go into Settings, Mail Contacts and celendars, Exchange, Account, then type your password in there
For some reason the automatic password prompt doesn't seem to work.
There is also no way to change your Active Directory password via iPad/Active Sync so if somebodies password expires when they only have their iPad with them they will get locked out of their account
Hope this helps