There are two reasons Internet Explorer will ask you for passwords. Either Internet Explorer is set to save your password and it has an incorrection password saved, or IE is set to prompt for passwords.
To stop IE asking for passwords where the password cached is incorrect, click the geat at the top right, click Internet Options, Click the Content tab, then Settings (under AutoComplete). Delete the AutoComplete history to get rid of incorrectly stored passwords and tick the Forms tickbox, then the User names and passwords on forms box to tell IE to remember the password next time you type it in.
In the event that this doesn’t fix the issue, it might be that you need to set Internet Explorer to not ask for your password for websites that have passthrough authentication. This would be for corporations only. To do this, click the geat at the top right, click Internet Options, Click the Security tab. Next, for each zone that has websites you want IE to stop asking for passwords on, select the zone (probably you only want to do this one the Local intranet and possibly Trusted sites zones), then click the Custom level button. Scroll right to the bottome of the settings list and select Automatic logon with current user name and password, then click OK.
If you are unable to make any of these changes or after making the changes they revert to the way they were, then it might be that your computer administrator has locked them down with group policy. You will have to ask your computer administrator to make the changes themselves.