Make sure its not Anemone Smut - starts with raised black blisters which burst, and the plant often blackens and dies back. Otherwise, it may be that they've dried out - they like free draining soil that doesn't dry out because they have surface roots, so longish dry spells without irrigation can cause this.

Loved the answer to this question! We have Japanese Anemone, it was here when we came. Wish mine would die back or just die! 'free draining soil', we are on clay! 'surface roots' when I dug up a bed of this, and threw on the bonfire, the roots went down more than the depth of the spade.
Sorry I don't actually know the answer to the question, I just spend my time trying to stop the ghastly stuff spreading out of the bed it's in, usually with the lawn mower.

Honeysuckle, it doesn't JUST have surface roots, obviously it goes down as well, and quite a long way, as anyone who's tried to dig out a healthy clump or three knows well. There are also a lot of roots just near the surface, like a sort of mat, which means it dries out a bit sharpish if the weather is dry and might cause these symptoms. Worth mentioning if the plant is in trouble as a possible cause, that's all.