Why can't I stay logged in on my iPhone?

If you have to log in every time you go to Full Slate on your iPhone despite having checked 'keep me logged in' on the login page, check your browser settings (under Settings > Safari) to see if 'Private Browsing' is turned 'On'.

If so, you'll need to turn this off in order to avoid logging in each time you visit Full Slate. More on how to do that here: https://support.apple.com/en-us/HT203036