What I've heard is that they continue to grow their entire life, but are mostly done at 3-5 years old.
We keep a large herd of Kiko/Boer crosses to assist with weed management for our cattle pastures. On the does, the horns are basically full grown by the time they're 3-4 years old, though it is possible that they are growing more, but not enough that I notice. With the bucks, we are always needing new genetics (because we're constantly keeping daughters to "breed up" the herd, to replace old and cull does), and so often buy a young weaned quality buck in the summer, use him for one or two seasons, and then sell him when he's 1-2+ years old. I had purchased a triplet buckling from a Kiko breeder four years ago and bottle raised him, and so recently contacted the person I sold him to, to ask how he was doing. The buck's doing great, the guy loves him, and uses him as his primary herdsire. He linked me to some pictures of him, and at 4 years old now, his horns are awesome! They're corkscrewed, and probably over 40" tip to tip, definitely bigger than when we sold him as a 2+ year old!