Chrome not asking to remember passwords

From Google's help:

Make Chrome ask to save passwords again

If you told Chrome to never offer to save your password for a specific site, but you change your mind, you can bring back the option.

1. On your computer, open Chrome.
2. At the top right, click More More and then Settings.
3. At the bottom, click Show advanced settings.
4. Under "Passwords and forms," click Manage passwords. A box will appear with a list of saved passwords.
5. In the "Never saved" section, select the website and click Delete Delete.
6. Click Done. If Chrome isn't asking to save any passwords anymore, you may have asked it to stop saving passwords. Bring back the prompt by turning "Offer to save your web passwords" back on.

Chrome isn't saving passwords If you've told Chrome to save a password but it's not showing up, try deleting and resaving it.

1. Open your list of saved passwords, and check for the website.
2. If the website is listed, delete the saved password.
3. Go to the website, and sign in.
4. To save your password, when prompted, select Save password or Yes.