I have to agree with Martinp on this one. I realize Jeremy runs the site, so the way he explains it should be the way it works. But in reality, I experience exactly what Martinp described.
For the most part, I log into GC.com from my laptop. I never log out. However, occasionally I login from the office computer. If I set the "Remember Me" box in the office, I then have to log back in the next time I go to GC.com from the laptop. If I just log in, but don't check "Remember Me" in the office, then I don't have to login again on the laptop.
I just chaulked it up to being something I could live with since I don't go back and forth that much. However, I could see it being a pain if someone switches often.
I do know it's not an IP issue as I have static IP at home where my office computer is located and when I take my laptop on the road, it doesn't "forget" me.
I am editing this post to retract all the above I put in grey. It seems something has changed since the last time I saved my login in the office. I just tried it again tonight, and both logins were saved. That is how it was doing a couple of months ago, however.