Disable the CB system plugin within Extensions > Plugin Manager and retest the Joomla login module to see if its Remember Me will work.
I don't know what to tell you. CB doesn't handle the login. Our authentication API does some processing such as finding a user, testing blocked/approved states, firing triggers, etc.. but the actual login is 100% Joomla. We send Joomlas login function the username, password, secret key, and remember inputs. I suppose there could be an issue with what value is being sent to Joomla for remember me, but it seams to be working ok here.
If you've any sort of extension that blocks cookies it's possible that's what's causing the remember me cookie to break.
Have you checked the Joomla.org forums to see if anyone else is having similar problems?
Ensure you're using CB 2.x nightly release found below as well to see if it solves your issues.
www.joomlapolis.com/downloads/doc_details/640-community-builder-nightly-build