I know how frustrating it can be. My first suggestion would be: "Be slow to act." Rule #62 and take it easy. Be kind. Don't do something that you or him will later regret.
Pain is our greatest motivation. It motivates us much more effectively than a sponsor can motivate us. His success in sobriety is not a reflection on you or your sobriety. What he does or doesn't do will not affect you or your sobriety -- unless you let it affect it.
Remember, that we can't get inside their heads. We might think we can, but we can't. He may be doing the best that he can do considering what he's got to work with (which is himself). We can often cause more damage by being too over-bearing on them. And, don't get and don't hold a resentment on him.
Our job as a sponsor is to be helpful to them. That's it. We can't control nor direct them. They are responsible for their own recovery and their own lives. Let him know that you are there to help him -- if and when he needs some direction. And, let it go at that. You don't have to end your friendship, Fellowship, or sponsorship of him.
Sometimes -- it sucks to be the sponsor. We think we know what they should and could be doing and it ticks us off if they aren't doing it -- "if" we let it tick us off.
My experience has been -- that the one's that we least think will make it -- often becomes the one's that we're someday proud of having something to do with helping them in the beginning.
1. "To show other alcoholics precisely how we have recovered is the
main purpose of this book." (That's also the job of the sponsor. We are the living, walking, breathing Big Book in front of them. And, we show them precisely how WE recovered).
2. "Many do not comprehend that the alcoholic is a very sick person." The person that's sponsoring has often made a lot of progress in recovery. Not always -- but often. We can get so far away from the problems of the past that we tend to forget that those that we're trying to help is a very sick person. And, we need to remember to treat them how we would treat a sick friend.
3. "And besides, we are sure that our way of living has its advantages for all." Be an enthusiastic good example in front of him -- of "our way of living." When he wants what we have -- he'll be more likely to ask for help.
I hope that helps. Best wishes.