The log in you have to do every time for this forum is not with Internet Explorer but it should be with the forum it self. When I log in there is a box that ask me to remember me and I check it and I don't log in again even when my PC shuts down. If I go to another PC I still have to log in since this is done with a cookie and every PC needs a cookie, but on the same PC log in once and forget it. If that doesn't work then you might have cookies disabled or something else that a more savvy member could help you with.
If you want Internet Explorer to remember passwords, open IE, top of page look for "tools", "Internet options", "content" tab, "auto complete", "settings", make sure you have the box checked for "users names and passwords on forms" and also check the box right under it " prompt me to save passwords"