The support of a dying patient can be one of the most difficult ministry arenas. For one thing, our culture 
denies death so rigorously. For another thing, pastors like to help solve problems and to have answers.
A pastor may feel helpless when he comes face-to-face with death. Death involves helping with the acceptance of the fact and how to cope, not in solving the problem. Death involves walking with a grieving person, and crying with them. And a third reason it is difficult to be present during death and grieving is because it encompasses such an emotionally charged atmosphere.
You too may have deep insecurities about being present during the dying process and feel inadequate when called to the hospital into such an emotionally charged atmosphere. We all have had moments when we feel inadequate, ill-prepared or overzealous to minister and do not come through in the best way.