According to your profile you use Ubuntu. The default browser in Ubuntu is firefox. So I'm guessing that you have a problem with firefox's password manager.
Does this happen for all sites or just a few?
Check and see if the website you want password saved to work on is listed in : password manager >passwords never saved . If so, just hit the remove button close out, and it should ask you to save the password next time you visit the site!
Are you allowing sites to set cookies?
Check you have 'Remember Passwords' ticked in Tools > Options > Privacy > Saved Passwords
If it is then try unchecking the remember passwords box, closing Firefox, then repeating the process, checking to put an "X" in the box once again, thereby setting the proper flag in the script file, so the remember passwords utility is re-enabled.