Firefox 3.5.3(latest version) is a buggy version. It has problems remembering passwords. As long as the browser is running it'll remember the user-name and password. But if you exit it and reopen the same website the user-name and passwords are forgotten and you'll have to type them again.
►Edit:
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▼Info Update▼
Bug Fix/Workaround method for Firefox 3.0+
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From http://www.techsupportforum.com/
Firefox 3.0+ stores cookies in a file called cookies.sqlite. These cookies include password/log-in info from sites that supply such - like VideoHelp.com
What has likely happened is that your cookies file is corrupt. Using Firefox's "Delete Cookies" to clear out cookie info won't be enough, because the cookies.sqlite file itself is still there and so are the problems. You must delete the entire file. Don't worry - Firefox will create a new version the next time you start up the browser.
To delete the cookie.sqlite file, first exit completely out of Firefox, then go to Windows Explorer. Place the following text into the Address Bar ..
C:\Documents and Settings\Owner\Application Data\Mozilla\Firefox\Profiles
You should then see an oddly named folder with .default as the extension name (if not, tell Explorer to show extension names).
Now, click-on this folder and look for the file cookies.sqlite, then delete it.
Suggestion - Before deleting the cookies file, write down the username and password info used at each site requiring them. Then after you delete the cookies file, re-enter Firefox, go to all the sites where you put in log-in info and re-enter all such info.
After this, exit out of Firefox, then go back to Windows Explorer and re-visit the folder where cookies.sqlite is and copy it to a different folder.
Now, if you should start having log-in problems again, just copy over the back-up file which will write over the current cookies.sqlite file. If you have joined new sites with log-in requirements since, then save such info accordingly and backup the cookies.sqlite file again.
I hope this one gets your problem solved.. :)
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