FYI: I don't know where their mobile app is pointing too but it works perfectly fine
I've given up and just started searching for 'bank of america' in the Maps app.
(iPhone app, 3gs.)
They fixed this is the latest release. It now will keep you logged in as long as the app hasn't been kicked out of memory (which is not up to them). On a 3GS that might be sooner than you'd like, but has been working for me on my 4.