This is HTTP Authentication and the iPad cannot "remember" the credentials of these sorts of logins. It has no problems with a normal web form however.
If you are happy to have your username and password stored in plain text on a bookmark in Safari however, there is a way to allow you to login without filling out those details again.
Just visit the site with the following formatted url :
Rememer to change the 3 obvious variables (username, password and domain). This should log you straight in. You can save this as a book mark and then use that going forward.
The username and password must be URL encoded if they contain any special characters.
Just remember that anyone who picks up your iPad could view the bookmarks and see the clear text username and password, so I wouldn't use this on your banks website :)
Hope this helps.