On all of my Rev3 and Rev5 BeagleBones, when I unplug the ethernet cable, the connection manager dies, thus disabling the network and making it impossible to reconnect anywhere.

I don't know why the connman service crashes, but for me the solution has just been to restart the service whenever it stops.

 

You can do that by just adding the following two lines to /lib/systemd/system/connman.service in the [Service] section: