Awww, I'm sorry to hear this about your Dad. It's hard to watch someone you love seem like they are suffering or having a bad struggle with something. That is very sweet that you are concerned for him. Divorce can be very difficult, even devastating. It might have really hurt your father when he got divorced from the person he thought he was going to spend the rest of his life with. It sounds like he really might be depressed. And it's not surprising that he doesn't want to see a doctor. I'm not sure how old your Dad is, but in my experience, most men, especially ones over 35 (younger men seem to be much more apt to seek professional assistance when something is wrong) do NOT want to see a doctor, psychologist, therapist, etc.

Maybe just have a frank discussion with him. Tell him what you've noticed and tell him you are concerned and want him to feel better. If he refuses to go to a doctor or other professional, you can't force him, but you could tell him you would view it as a favor to you. Of course let him know you love him and support him.