Call Hospice. When a friend of mine was sick they had great respite care, for his mother! She was doing so much she was burned out, they had someone trained in end-of-life care to watch my friend while his mother was able to get out and just have some time for herself.
Outside of hospice (have you left a message on their machine yet *hint hint* I recommend you look into getting some professional help in there. If you are burnt out and tired, you won't have the quality time with your dad that you wanted once he has passed on. This is from personal experience.