Make sure that you do not run Firefox in permanent Private Browsing mode.

• https://support.mozilla.com/kb/Private+Browsing
• You enter Private Browsing mode if you select: Tools > Options > Privacy > History: Firefox will: "Never Remember History"
• To see all History and Cookie settings, choose: Tools > Options > Privacy, choose the setting Firefox will: Use custom settings for history
• Deselect: [ ] "Permanent Private Browsing mode"

i don't use it in this mode...

Do you mean names and passwords in the Password Manager or do you mean that you are no longer logged on to (remembered by) websites after closing and restarting Firefox?

There is a difference between remembering the name and password in the Password Manager and a "remember me" check box on a web page.
The latter usually involves the creation of a special "remember me" cookie that is stored on your computer and that is send to the server.
If that "remember me" cookie is removed or gets corrupted or is not send to the server then the server won't remember you and you need to sign in once again.

• http://kb.mozillazine.org/Cookies
• http://kb.mozillazine.org/Password_Manager

One more time i will explane to make it clear..

My firefox 7 does not askes me "do you want firefox remember password on this website"

Mean that when i enter to new web site with password and username priority, when i enter them Firefox - whis have to ask me rememmber the password or not- does not askes me ..

On my settings "rememmber passwords" box is checked. i don't mean on the web site.

Start Firefox in Diagnose Firefox issues using Troubleshoot Mode to check if one of the extensions is causing the problem (switch to the DEFAULT theme: Firefox (Tools) > Add-ons > Appearance/Themes).

• Don't make any changes on the Safe mode start window.
• https://support.mozilla.com/kb/Safe+Mode

• https://support.mozilla.com/kb/Troubleshooting+extensions+and+themes

it is just don't showing "remember password" in firefox 7 for secure https sites. while in older version there was a way to change the ntLoginManager.js to enable this feature. Any way in firefox 7 to enable this??

-> click Firefox button and click Options

• Privacy panel -> History section -> under Firefox will: select "Use Custom Settings for History"
  • Remove Checkmarks from:
    1. Always use Private Browsing mode
    2. Clear History when Firefox Closes
  • place Checkmarks on:
    1. Remember my Browsing History
    2. Remember Download History
    3. Remember Search and Form History
    4. Accept Cookies from sites -> click Exceptions button and click Remove button for all entries which have Status set to other than Allow -> Now type addresses of websites whose Cookies you want to be stored by Firefox e.g. mail.live.com , login.live.com , hotmail.com , msn.com , mail.yahoo.com , login.yahoo.com , yahoo.com , mail.google.com , google.com , etc. & click Allow button for each of these websites (One by One)
    5. Accept Third-party Cookies -> under Keep Until : select They Expire -> click Close

• Security panel -> place Checkmark on Remember Passwords for sites -> click Exceptions... button and click Remove All button -> click Close

-> Click OK on Options window -> Restart Firefox

-> IF your Username & Password is already stored by Firefox, you need to Delete it

• Deleting Passwords
• https://support.mozilla.com/en-US/kb/make-firefox-remember-usernames-and-passwords#w_viewing-and-deleting-passwords

-> IF your Username & Password is not currently stored by Firefox yet, go to the Website

• Enter Username & Password
• on the website, place Checkmark on Keep Me Signed-in or Remember Me option
• click Log-in or Sign-in button (see attached Screenshots #2, #3)
• Firefox will ask if you want Firefox to Remember your Username & Password (see attached screenshot#1) on this site
• click the Remember Password button

Check and tell if its working.

-> IF you use Clear Recent History feature, DO NOT select Cookies, Forms and Search History, Active Logins, Site Preferences

• https://support.mozilla.com/en-US/kb/Clear%20Recent%20History#w_what-things-are-included-in-my-history

-> IF you use Privacy Cleanup softwares like CCleaner etc., DON'T SELECT FIREFOX IN ITS SETTINGS. These softwares can be responsible for Deleting your Firefox Settings.

You can remove autocomplete=off with a bookmarklet to make Firefox save the name and password on websites that use autocomplete=off to prevent Firefox from saving the name and password.

• http://kb.mozillazine.org/User_name_and_password_not_remembered

You can use this extension if you want to add a name and password manually on sites were Firefox doesn't offer to store it.

• Saved Password Editor: https://addons.mozilla.org/firefox/addon/saved-password-editor/