I am also having problems with BBM on wifi since the update to 10.0.10.85 the messages won't send or will sit there for 5 min then send. It's like I will have a connection for a short span then it goes away. BBM voice or video usually shows network connection error on wifi. Receiving updates and messages on wifi is rare. If I turn off wifi I have no problem it will send and receive instantly. Prior to update BBM voice and video on wifi was no problem. And non of my other devices such as my PlayBook have problems on wifi. Very frustrating. I tried changing settings on my wifi and phone to 2.4ghz and 5 ghz Instead of dual band as indicated on other post. But no luck or will work for short periods. I even cleared my phone and reinstalled and no difference.
I have had intermittent BBM problems with all versions of the OS when on wifi mostly although yesterday I had no BBM even though the wifi was off. What I tried yesterday was shutting off my mobile signal for 30 seconds yesterday and then turning the mobile signal back on. When the signal was turned back on then BBM was working again. BBM drops intermittently. Sometimes it works for a whole day and then vanishes.