There are so many ways of making your password remembered in yahoo mail..like
Some of them are..
1.AI Roboform Toolbar with Firefox
NOTE: “You need to download and install RoboForm to use extension.”
Description: RoboForm is Top-rated Password Manager and Web Form Filler that completely automates password entering and form filling.
Features:
- Memorizes your passwords and Logs You In automatically.
- Fills long registration and checkout forms with one click.
- Encrypts your passwords to achieve complete security.
- Generates random passwords that hackers cannot guess.
- Backs up your passwords, Copies them between computers.
- Gives you one set of bookmarks and passwords for
IE, Firefox, Mozilla, AOL, MSN, Avant, MaxThon browsers.
Download Roboform
2.A Script for greasemonkey thats automatically remembers the password for yahoo mail.
Description: Enables autocomplete for https://login.yahoo.com/ you need to install this script in grease monkey and thats all.
Download GreaseMonkey For Firefox
3. Use Sxipper to Remember your usernames and passwords
Description: Sxipper is a free plug-in for Firefox that lets you log into any website with a single click. Sxipper saves you time by keeping track of all of your user IDs, passwords, and the personal data you share every day over the web. Sxipper logs you in securely and helps to prevent you from being victimized by phishing sites and phony logins
Download or Install Sxipper Plugin For Firefox
I hope some of the above may be able to solve your problem..