Curtaincall- I cared for my grandmother after she had a stoke. She was in her mid-80's at the time. She has always been quite small but she developed what I completely unscientifically called "old lady anorexia". You would put a meal in front of her and she would state "I couldn't possibly eat that much". You had to be really sneaky to get enough food into her- repeated plates of small portions, leaving bowls of her favorite candies to snack on to increase her appetite, using Ensure or Complan type drinks.
It was very important that my grandmother didn't lose much weight has she was bipolar (two psychotic episodes as well, sectioned twice) and she took lithium. If she lost too much weight the lithium would start to affect the muscles in her throat and she couldn't speak. She was hospitalized once for this.
Unlike you mother, she was the old and infirm one. But I can see that had she been the younger, stronger half of the couple a situation to that of your parents could have occured, although I'm not saying that is the case.
If your parents are that closed off I do think that you need to escalate this somehow, even with social services if you can't find their GP. While it's entirely possible that you father's weight lose is a result of recent illness, at his age this is a significant risk to his health.
You are obviously a caring daughter and want to do the right thing, even though in this case it may be the hard thing. It's an incredibly difficult transition when we have to be the ones to take care of our parents.