In the Chrome you can choose Save or Never.
If you choose Save, next time when you log in, you don't need to enter the password again.
And if you choose Never, next time when you log in of course you need to enter your password, and the notification for asking to save password will not appear again.
If you already chose Never and now you change your mind and want to save your password for easy log in.
1. Log in as usual, write/fill username and password.
2. See at the right-side of address bar, you will see a key symbol.
3. Click on it (key symbol), and then you will see the option to save the password. Click Save to save the password.