I don't milk my does, but I would say at least a couple of months. I weaned my meat kids last summer and a doeling found a hole about a month later. Her mother had dried off, but that didn't stop the doeling from trying to nurse.
It totally depends on the doe, and the kids. I had a doe that if you took her kids away for anything more than two weeks and put them back, even if she was being milked, she wouldn't let them nurse at all. She would beat the snot out of them if they tried, but they would TRYTRYTRY and she would spend a week running from them if i didn't separate them back out. Most of my kid/doe combinations it took months, though. Baby would want to nurse, mom would let her... The only one i really REALLY wanted to put back in to my herd as a milker took over six months. It wasn't until her mom was completely dried off that she stopped trying completely.