Sometimes when I sign out of Gmail...
 

It decides to stay logged onto my "google account" or something. I find this incredibly annoying, because then I have to go sign out of that.

Does this happen to anyone else, and is there a way to stop it?

It has never happened to me, logging out of anything google has resulted in a global google account log off all the time.

Clear your cookies and untick the "stay signed in" box?

http://i137.photobucket.com/albums/q...505643_n-1.jpg

But nah, that's not the issue.