But that's the odd thing, it does. I haven't logged into FlynnLives since last month, I visited last night to find out if my login still works and it automatically logged in. So, it's not a cookie problem.
I think it may have been the format they used for the game. As I was playing, there were a couple of glitches the game had (for example, it had the level menu up over a game play while I was playing and it occasionally skipped levels when I clicked on the "Next Level" link after winning the level)
Have you tried completely logging out of FlynnLives and then logging back in?
I'm on a Mac using the current version of Safari and encountered zero issues. What OS and browser are you using?