I have issues with wifi driver on my Kubuntu 16.04. bcmwl works fine with 4.4.0-31-generic (the oldest version of kernel on my system), but when kernel updates to different version list of wifi connections disappears. Previously i've fixed this by loading 4.4.0-31-generic and reinstalling bcmwl-kernel-source from pool on Ubuntu installation stick. After reboot on newer kernel version Wifi worked like a charm, but now this trick did not work. I thought about restricting dkms to rebuild bcmwl during the upgrade, but do not know how to do it. Any ideas how to fix this?
Maybe the issue is about that kernel in particular? Why don't you try updating to the latest kernels? like 4.8 or 4.9? The application: Ukuu (Ukuu kernel update utility)