I highly doubt RIM will go bankrupt anytime soon. The main reason of why they are failing right now is because of their marketing strategy. They aren't advertising their products like they should. The company is still doing pretty good, but they won't be going bankrupt anytime soon.
will rim go bankrupt?
if it does will bbm stop working?
They're in a pretty bad place right now. They're most likely using the new OS from the Playbook for the phones, which may help them. They may also buy WebOS from HP, be bought by someone else, or go bankrupt. Not sure if BBM would stop working as the carriers might step in and support it. Only time will tell.
RIM is not doing well in North America but in emerging markets in Africa and Asia they are showing enormous growth. In other words they aren't going bankrupt anytime shortly.