Weird problem

I can't seem to stay logged in at tthfanfic.org, which uses cookies timed so that you need to log in every two weeks. Instead they appear to be set to expire at the end of sessions. I presume this has something to do with the new PC, Firefox, etc. but everything else is OK so I'm a bit baffled. Any suggestions.

Before anyone asks, I've tried deleting cookies, logging in and out, changing password, etc. but nothing seems to work. Any suggestions?

Update on the browser problem

Finally got round to trying some other browsers and PCs.

This is also happening with Safari and Internet Exploiter on the Windows 7 box, but Chrome seems to be OK. I'll check it again tomorrow and make sure I'm still logged in.

It's also happening on my iPad.

It isn't happening on my iBook or the old XP box with any browser.

I really have no idea what all this means - some sort of problem with a particular sort of browser architecture?