I just got a windows tablet on black thurs and had the same issue. I currently am logged into Google on my nexus 5 phone and laptop. I downloaded chrome for the tablet because I don't like explorer. logged into Google & was prompted to recover/reset password. No idea why because my password was the same as always. I reset it, then was kicked out of my account on my laptop.. Dist password reset again on the laptop, then logged out of Google on the tablet. Then came the nightmare, my phone kept popping up the password reset prompt in a vicious cycle, it kept popping up so quickly that I couldn't type in the CAPTCHA fast enough. I ended up managing to open my notepad app and copy/pasted my password into the prompt screen. It seriously took like 20 min to do this.
I ended up making a whole new Google/gmail account to use specifically on my tablet. I'm ok with this bc I don't need my browser & photos synching anyway, I plan to use the tablet more for general internet browsing and streaming. The only thing I can think of is maybe Google only allows a max of 2 devices logged in at once? it's super annoying if that's true.. I'm going to research more online & will post here if I find any answers.
EDIT: ok so I realize your issue is with an android device not windows, but it may still be the same issue because it involves Google accounts (the fact that one of my devices is windows is prob irrelevant)