David,
So what excuse did he give you? Just because you cannot stop him from drinking, does not mean you can't get him to a dentist. You say the man is a good handyman so some of the time he must be sober enough to understand what you are saying. Men hate and fear dentists so he may not have been passed out drunk, just not willing to go to dentist. I wouldn't make him another appointment, but would offer to pay for his first treatment or whatever arrangement you had made with him about payment. Give him the dentist name and phone number and see if he will make his own appt. Might be worth a try.

Take care,
Eileen