He is using the threat of suicide to keep you in his life. If you are truly concerned about him attempting suicide, then whenever he calls making his threats, call the cops and give them his location. You may be a doctor but you are ill-equiped to deal with this situation. IF he is serious about suicide, then he'll receive psycho-social support and be under supervision. If he isn't then he'll think twice about calling you to make empty threats.
Just as you are not responsible for the way he CHOOSES to live his life, you are not responsible for whether or not he chooses to end his life. It all belongs to him, and if you let him manipulate you in this way, you'll get dragged down with him. Who's going to take care of you if you don't?