If your dad is losing his hair, you can describe him as balding — although it may hurt his feelings if he's sensitive about his looks.
Someone who's balding is well on his way to being bald. He may have a shiny bald patch on the back of his head or just extremely thin wisps of hair all over — either way, he's balding. Both balding and bald probably originated from the Celtic root word bal, which means "white patch or blaze," especially one that's found on a horse or another animal's head.