That’s because the form on that page has autocomplete set off. If you view source and search for ”<form”, you’ll see the tag and its autocomplete=“off” attribute. What that attribute does is request that the browser not offer to save the username/password for that form/URL.
The site’s designers probably put that there as a security measure, like to keep the clueless from saving their usernames & passwords when using public computers.
Anyhow, if you get Firefox to save the username/password just once, it will auto-fill them for you each time you visit the page, in spite of the autocomplete=“off”. And fortunately, you can use a “bookmarklet” to get rid of the autocomplete attribute in the DOM, which will basically make it as though the site’s designers had never put that attribute there at all.
Bookmarklets are just a way of running some JavaScript on a page, using a bookmark to store the script. They’re basically just bookmarks that use a “javascript:” URL instead of an “http:” URL.
So here’s what you do: browse to https://www.squarefree.com/bookmarklets/forms.html and drag the “remember password” to your bookmarks toolbar (if it’s not showing, use View > Toolbars > Bookmarks Toolbar to turn it on). Then when you browse to your school’s site, click the “remember password” bookmark that’s now in your toolbar; you’ll get a popup stating that autocomplete was removed from 1 form. Then fill in your username and password as usual, click Go to log in, and Firefox should offer to remember the username/password for you.