I do not store passwords inside internet browsers as I prefer to use utilities particularly designed
for secure personal data management. Firefox password prompt is very annoying,
so disable it once for all and use KeePassX or similar software.

Open Preferences window.

Firefox - main window

Firefox – main window

Choose Security settings.

Firefox - preferences window

Firefox – preferences window

Disable Remember logins for sites under Logins.

Firefox - security settings

Firefox – security settings

Done.