I use the Game Editor a lot on this site (it's linked to the Analysis Board) & I've noticed it displays a green board when I'm logged off but the brown one when I'm logged in - just one of the many quirks of this site !
But your main problem is that you are being logged off the site automatically & it's the second case of this I've come across in the last hour, although it's never happened to me.
Worth checking to make sure your browser & Java are updated to the latest versions. You might also re-post this on the help & support forum - you'll probably get more of a response than here ...
http://www.chess.com/forum/category/help-support
But if you want, you can always report it directly to the staff...
http://support.chess.com/Tickets/Submit
Good luck with that.
I'm having a problem with the analysis board for on-line chess. It opens when I click "Analysis" and I get my preferred brown squared board. When I make a new move on it, however, it's replaced by a green squared board (still of my game) and I've been logged off! I can do my analysis but then have to log back on again. It used to work fine and I haven't changed any of my settings. Anybody else experienced this? Help please.