I'm another one who is being prompted to logon every day.
I always use the "view new posts" option, which is when I now get the logon prompt.
I then select this thread, and when I want to post this message I am prompted to logon again.
Sometimes logging on via the top/right box does not work, and it kicks me out to the full screen logon page, but this is not consistent, sometimes yes, sometimes no. Some days it won't let me logon at all, but if I return a few hours later I am successful.
I've done the whole delete cookies thing. I've even cleared LL completely from my Favourites, cleared all temp files, and re-loaded LL, still no joy. It just cannot seem to remember me.
Never had any of these issues prior to the recent changes. Been a member for years.