I'm one of those who have a few SO pages open all day. I usually just hibernate my machine (I hardly ever reboot) and often hit the reload button for two pages (questions and responses) several times an hour.
Now, for the last one or two weeks (I think), I keep getting logged out of SO about once or twice a day while I reload. I hit the reload button (key, actually) for the two pages, and one of them indicates I'm out. If I then reload any of the other SO pages I have open, I'm out there, too. (I know that's, um, likely, but I had to say it anyway, right?) I hit the "login" link, Google logs me back in, and that's that.
I have no idea what makes these times different than the other times I reload. I haven't seen a correlation of this to anything. It just happens.
I do remember following Jeff's advice on how to create a Google profile so that transition between the sites gets better, but I cannot, for the live of me, remember whether I did this before or after this problem appeared for the first time.
FTR, I have seen Keep getting logged out of Chrome dev, Keep getting logged out of StackOverflow today, and I Can’t Log In With My OpenID — Troubleshooting Tips and it didn't help.