Pretty much the same thing happened to me. Once I reached my goal and dropped to two milligrams a week the urge to drink returned, though not in any extreme way, just more than the total indifference I felt at the higher dose. Naltrexone might be worth looking into instead since it reduces the dopamine reward from drinking and can lower the pull to keep going.
After ten months on this medication I have transformed my body and reached twelve percent body fat without needing to lose any more. As I taper from a peak of four milligrams weekly down to one milligram the desire to drink has started coming back, something that was completely absent for the whole ten months. When I do drink now it also brings urges for other substances I had problems with years ago, so I am wondering whether staying on a low dose would keep those cravings under control. Has anyone else seen this happen?