My dad is like that, too. Can't ride his bike anymore, walks as if he was half-drunk, loses his balance and falls sometimes, yet absolutely refuses to get checked out by a specialist. It is highly frustrating for the rest of the family. In my dad's case, I'm thinking that one of the reasons why he is refusing treatment might be that he's clinically depressed and has lost the will to live.
At any rate, I feel for you. Maybe, although it's not a pleasant thought, it will take a medical emergency (a minor one, hopefully!) for the person to have to go to a hospital, where they will routinely get a full check-up. Still, it's very frustrating to be forced to just stand by and watch, so I can relate to what you're going through. Hang in there!