Notice that there is no mention of diet because diet doesn't matter that much as long as there is a surplus. The body is pretty amazing.
You're strongly implying causation here. I'm unaware of any serious body of research that indicates elderly people are getting frailer because of a decrease in appetite.
> A decline in physical activity, common among older people, is only one reason sarcopenia happens. Other contributing factors include hormonal changes, chronic illness, body-wide inflammation and poor nutrition.
It's wasn't a major cause of muscle loss.