I recommend using the following extension:
Multifox is an extension that allows Firefox to connect to websites using different user names. Simultaneously!
For example, if you have multiple Gmail accounts, you can open them all at the same time. Each Firefox window, managed by Multifox, accesses an account without interfering each other
Each Multifox window is flagged with a number indicating the identity profile. Logins made in windows with different numbers are isolated.
Logins are preserved the same way they are in “regular” windows. Even if you close the window or quit Firefox.
The identity profile of each window is preserved when Firefox restores the session.
It can also easily switch between profiles:
Just use a different profile for each Gmail account you have, and Multifox should remember it all. There should be no need for re-logging in when using multiple accounts with Multifox.
About Firefox not asking to remember the password for multiple accounts, I have not experienced that issue with Multifox. I also use the extension, Secure Login, but am not sure if it will help. Secure Login makes auto-logging in with remembered password much easier, so I recommend you install that too, regardless. I'm listing some of its features that may be useful in your case:
- Login with one click or a keyboard shortcut (automatically submitting the login forms).
- Easy and convenient selection for multiple logins (multiple users)
- Integrates with Mozilla Firefox password manager.
- Provides easy access to the saved passwords.
- Shows the login URL(s) and the number of available logins in a tooltip of the toolbar button and the statusbar icon.