Robots.txt not updating

Once I experienced the same issue, this is what I did to fix the issue.

Edit the robots.txt file directly (using FTP/SSH),

User-agent: * 
Disallow: /wp-admin/ 
Disallow: /wp-includes/

There are two reasons if the robots files not updated when you edited using a plugin.

1. File permission.
2. Some other plugin is reverting the changes.

Also try to update the search engine visibility settings (this might not be an issue, but just have a look).

Settings -> Reading -> Search Engine Visibility (Uncheck this option) -> Save

I hope this helps.