I stay logged into SO from multiple computers at my location using my Google ID.
Today, for some reason, multiple times from the same multiple computers, I'm getting repeatedly bumped out and having to click the "login" link. Selecting the "Google ID" icon gets me back in quickly.
Not really a big deal, but very unusual to have this happen many times in one day after staying logged in for many days/months/etc. without this issue.
EDIT 2/13/13: I've un-accepted my answer from below because this issue continues worse than ever. I've been kicked out at least eight times today from each of my computers.
EDIT 2/14/13: What do we need to do to get some attention to this problem?... (EDIT: the tone is not meant any other way than how it's written... I honestly want to know how to properly report this problem) today it's much worse than yesterday, I'm getting bumped out hourly now. I've un-accepted my answer and that didn't work, but posting a new question would not be proper.
EDIT 2/22/13: Starting to notice a pattern. If I move from one machine to another, I get bumped out of the previous machine. So it appears that the real issue is that I cannot stay logged in from multiple locations simultaneously. Again, previous to 2/9/13, staying logged in indefinitely from as many locations as I wished was never an issue. So what can be done? I'm not going to abuse this site by posting multiple threads, but this seems to be getting no attention from anyone that cares to investigate.
EDIT 2/27/13: Still happening very frequently. Today I created and added a new "Stack Exchange" login to my account and stopped using my Google ID. I dumped my cache and all cookies. That was only a couple of hours ago, and I've already been logged out three times since. That also blows my 2/22 theory out of the water since I've stayed with one machine this whole time too.