You can remove dead wood at any time as it is no longer productive to the plants health. You have had a very long run with these shrubs and they may be declining from age and nothing more. Wilting leaves in the middle of the summer may indicate just a lack of water or a problem with the roots or crown of the plant. Burning Bush is a favorite of rabbits so there could be physical damage. fior a more focus response, call your local Extension Office to find out if there is a local problem.