The problems I've experienced are all on my iPhone - I can log in successfully, and I can read a number of threads, but as soon as I click on another member's name to go to their profile page with the intention of sending them a PM, I am logged out. I attempt to log in again, and repeat the exercise, only to find myself logged out every time I try to send a PM. What I find unusual is that I can log in and read numerous threads, remaining logged in. It's only when I visit a member's profile page that BPL considers me logged out.
I do not experience this on any other platform - this is not repeatable in Safari on Mac OSX 10.6, nor does it happen in Firefox on Windows 7.