Ok here is the thing... BlackBerry OS 10.3.0.296 on Z10 with the latest leak if BBM. The problem is BBM only works on wifi- which is highly annoying. I am in a move all the time - so BBM is useless to me now. Logged in with my iphone/android using the same sim card and there is no problems or whatsoever.
Did not help :/ I have upgraded to the latest bbm available believing that's going to help. Might downgrade the whole OS as you suggested to check if that makes any difference. Never payed to much attention to BBM as all my friends are on what's app, Viber etc.