I'd be surprised if the summer drought is responsible for the die back. Cistus grow in hot, dry Mediterranean areas. I thought they liked light pruning - like lavenders. They do deteriorate relatively quickly and cuttings should be taken every. three or four years to replace the mother plant. I think the plant might be on its way out. You might as well cut out the dead wood anyway, you have nothing to lose, but scratch the bark with your thumb nail first to see if it is green underneath. If so, it isn't dead. Just a long shot, could a dog have cocked its leg over it and scorched the centre?
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How do you acknowledge Easter.