Outlook.com/live.com signin will not remember password or email address

My browser isn't remembering the email or password for the login page at live.com, either for outlook.com email or the login for MS Answers. The password manager for Firefox is working on other sites (it asks me if I want it to save new passwords, and it inserts the password for sites already saved). I do have the same problem, whether in Firefox or Internet Explorer. Cookie management doesn’t seem to matter. This problem exists regardless of whether I clear out cookies, or have them saved.