To help you with your problem, please check out some of the settings you have in FireFox Tools, Options:
On Privacy Tab make sure you DON'T have a check mark in the box reading Always Clear My Private Data When Closing FireFox, and a DO HAVE a check mark in Always Ask Me Before Clearing Private Data. Then still right there click the Settings Button. Make sure there is NO check mark in Saved Passwords. Then go to the Security Tab. Be sure there is a check mark in Remember Passwords for Sites. Click the Exceptions button to be sure the sites you want to save passwords for are NOT listed there. If they are, remove them.
If you fail,please provide us more detailed information about the problem,we will try our best to help you solve it.