I nursed my youngest until he was 3.5, but it was only at naptimes and bedtimes at that point, and occasionally when he was sick or hurt himself. Around three, we went through a similar thing. I did have to go through a stage where I just said that now was not a good time to nurse. I had to be very firm about it. He would usually be muley about it if he felt like I wasn't paying him enough attention, so I'd try to get him involved in whatever I was doing if it was possible. If I was doing dishes, I'd give him stuff to dry or let him play in the bubbles. But sometimes he just wasn't satisfied with that, and there were tears. During that time I did make sure he got lots of extra snuggles and reading time, so that even though I was cutting down on nursing, he was still getting a lot of physical comfort.
As far as how much you need to be nursing to still product milk, I think it's very individual. I had milk, more than a drop or two for 6 months after ds3 weened and then I could express a couple of drops up to a year after!