to update (unfortunately, to add problems to the list)
I didn't have this problem when we first switched. I logged in, and was fine - logged in forever, so issues. Yesterday, I had to log out to use the Site Admin Team account. Now, after I've logged back into my personal account, I cannot stay logged in.
If I am on this window, and open a new BW tab - the index page, for example, I may or may not still be logged in on that next tab. If I click on a link within a thread, that thread will open in a new tab, and I am no longer logged in on that tab. To make it even more fun, if I do log in, it kicks me off that thread to the BW index page.
I seem to have about a 5-minute window (or 30 seconds) where things work as expected. Then, all login bets are off.
I did clear my cache and cookies and restart my browser. Issues seem to happen whether in firefox or chrome.