Answer: Dropmore honeysuckle is a large vine, and it will continue blooming all summer on the new growth. The best time to prune it is in early spring when you can prune it back as hard as needed. During the summer it is better to selectively prune just the occasional wayward tip.
Dwarf Korean lilac can be pruned immediately after it blooms, however it does not require regular pruning and naturally has a fairly symmetrical outline. This plant does not usually suffer from pest or disease problems so I am a little surprised you are seeing dieback. I would suggest you consult with your local county extension and/or professionally trained nurseryman to see if they can give you a specific diagnosis and then knowing that, suggest how to proceed.
I hope it is nothing serious.
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