I am not sure on the time, but the auto log out is as a result of trying to keep Chat as secure as possible.
In chat you can get bumped pretty quickly, particularly on mobile devices. As a consequence, the same happens on the forum. (We could not boot users from chat and keep them logged in on the forum).
I have noticed also that if I log in on my phone while logged in to desktop, I get booted. Also swapping networks, say from 4G to Wifi, i get booted also.