This was probably the worst case. One day this beautiful plant just decided to die. First it dried off all the new leaves so that the growing points looked like nothing will ever grow out of them again. Then it cast off some of the old ones. All that remained looked brownish and more like a carcass than a living plant (you can still see it on the picture). A very sad sight.
But just like it spontaneously decided to die, it then found the will to live. "Hey I forgot that I don't actually need those old growing points to start growing again!" And there there were three new branches! I think it should recover now. :)
Its mate is doing fine, btw.