Dieback is not a specific disease and can be caused by several factors including - frost/wind burn, canker at the base of the stem, waterlogging, mildew or black spot. Yellow and orange varieties of roses are more susceptible than other colours. A common cause is a deficiency in potash, calcium, phosphates and boron. A spring feed is essential if dieback is a problem.
For a well balanced granular rose food with trace elements use Toprose. Cut out the affected area afew inches below the damage and paint those pruned areas with Arbrex Seal and Heal.