• Websites remembering you and automatically log you in is stored in a cookie.
• You need an allow cookie exception (Tools > Options > Privacy > Cookies: Exceptions) to keep that cookie, especially for secure websites and if you let cookies expire when Firefox closes
• Make sure that you do not use Delete browsing, search and download history on Firefox to clear the "Cookies" and the "Site Preferences"
• Make sure that you not run Firefox in (permanent) Private Browsing - Use Firefox without saving history mode

See also Password manager - Remember, delete, change and import saved passwords in Firefox

Other things that need attention, see http://www.mozilla.com/plugincheck/

Your above posted system details show outdated plugin(s) with known security and stability risks that you should update.

1. Shockwave Flash 10.0 r45
2. Java Plug-in 1.4.2 for Netscape Navigator (DLL Helper)

Update the Java plugin to the latest version.

• http://java.sun.com/javase/downloads/index.jsp (Java Platform: Download JRE)

Update the Flash plugin to the latest version.

• http://www.adobe.com/software/flash/about/

Thank for your help firefox is remembering my past word now .put i lost the home page how do i get that back.....

See How to set the home page - Firefox supports multiple home pages separated by '|' symbols

If you can't keep the home page then also see http://kb.mozillazine.org/Preferences_not_saved

the only way i can get my firefox home page is to autumatically start firefox in a private browsing session.. then it dont remember my past words ..how do i fix this

this is what missed up firefox on me i downloaed stopzilla spire ware it scan my computer but i didnt like it ..so i removed it and after that firefox was missed up now i cant get it fix