After setting "Block Cookies" to YES, I am thrown out of the admin area and have to log back in.
Why does it happen?
This is because you don't click on the "Accept" button in the cookies notification bar, and the website does not save any cookie on your browser to give you an admin session cookie.
How to fix it
You should accept the cookies at the front-end of your website to avoid this situation or set the "Allow Session Cookies" to "Yes" and you will be logged in even if you don't click on the Accept button.