I am the only one that no matter how many times I tell it to save my username and password I need to re-enter in every single day. Its a wee bit annoying...
On Sony's site? Yeah, it doesn't like to remember people having logged in, despite being told to do so. It's not just you. Either over-paranoid or just bad login management. I'm not sure which.
I'm in the middle - I use FF, clean my cookies once a month, have the box checked on SOE's site, and sometimes (not as often as the op) it loses my auto-login.
Well since it doesn't seem to be limited to any particular browser; I suspect its some form of internet security/privacy software playing shenanigans with the cookies from the soe site. Norton Internet Prison and McAfee Internet Asylum seem to be the usual suspects. Zone Alarm can also get a little overly protective at times.
Try disabling these internet condoms and see if you can reproduce the problem.