I had some kind of google password issue during the week which required me t change my google password (a few people did). My shield now stops after about 20 mins and requires me to veryfy myself. I have tried everything i can think of including a factory wipe of the device. Anyone any ideas? I love this device but its completely yseless to me currently.
Create a new google account and use it then you know if it is the device or your current google account.
Turned out my issue was an andriod system (nvidia shield) was on top of an andriod tv (sony). Thanks - i would never have worked this out for myself!!
Try setting up an App Password. https://support.google.com/mail/answer/185833?hl=en-GB
Short version: You generate a specialized randomly generated password that can be used by specific apps and devices and it bypasses things like 2 factor. You can have many app-passwords and also revoke them without having to change your main password.
Just a thought... Are you using your Shield on an Android TV (Hisense, Sony etc.)? I had a similar problem until I figured out it was my TV doing that and not the shield ( I had forgotten to login on the TV).