Another pic...

You could try spraying it with draconil or a copper sulfate spray. I would check to see if your soil is too water retentive. You might need a faster draining soil. and try not to get water on the leaves when you water and do not water in the evening when it will stay wet on the leaves through the night. I just last a E . lilacina to that.

This post was edited by wantonamara on Mon, Sep 2, 13 at 11:50

Thanks for the tips! I think in future I'll also be more aggressive about removing diseased tissue before it has a chance to spread.

I took a photo to a succulent store here and they say that this kalanchoe is for some reason particularly prone to problems.