I frequently leave my client running, doing :lo and then relogging, sometimes as a different character. When I do this often enough, the game will become unplayably sluggish after one more login - often with the same character as the previous one. I suspect a resource leak.
I mention the changes of character - different accounts too - in case the resource leak is there, rather than in the log out/relogin sequence. (I.e. clicking "forget me" might be the problem.)
Note by the way that "remember me" and "forget me" behave really strangely if one has multiple copies of the client open on the same comp., as I usually do. If two chars log out within about 5 min. of each other, both clients "remember" the same one.