How to stop "Couldn't sign in" notifications? I have my Nexus 9 (on 5.x) connected to my iCloud account for email. It works fine, I even get notifications for new email. It can connect to the server just fine.

However, I get notifications from Gmail around every 15-20 minutes saying "Couldn't sign in" with my iCloud email address. 

I don't like my tablet and wrist vibrating that often with useless notifications. How can I turn these off (or, ideally, fix the problem) without turning off notifications for real email?
Did you try to disconnect and connect again the iCloud account with Gmail app? If the problem is still there, you could try to use a different app: with your setup you should have (maybe disabled) a so called 'Email' app.