jeanne has hit the nail on the head (or ass on the cheek if you prefer.)

If you are someone's submissve (including slaves) and you haven't revealed you are a tea-totaller or the equivalent before now, you've entered into the relationship unwisely or under false pretenses.

Worse still, if we're actually talking about a medical condition, (including alcoholism.)

In either of the above circumstances, I suggest you both reevaluate your currently suitability to the lifestyle of submission. You have a lot of growing to do still.

But I suspect that is not the actual case.

If this is not the first time the issue has come up, if the "limit" has been discussed but not agreed upon, and the submissive is making his or her stand in this manner, you have other issues to deal with, and they are severe, in my opinion, because there has been a breakdown in the nature of the D/s relationship.

Consider what you have done. You have pre-empted the dominant. Wrested away choice. Wrested away control. And demonstrated you don't trust him in this matter. Where's the submission? Especially as you will always have the option to refuse (and if it is important enough to him to insist, you have the right to end the D/s nature of the relationship, if not the whole relationship.)