Replacing the cement board is not realistic, I don't know of anything that may be more flexible and not deteriorate so quickly.
100% Silicone Caulk - White.
there are some colored cement repair products that contain silicone that may work good, also you can just use white silicone or caulk just squeeze it in and let it dry have a rag handy for cleanup both are flexible and last a long time.
Even if you use silicone tub-n-tile sealer you’ll need to figure out where to apply weight to cause the floor to flex upward. Apply the weight to flex the floor upward apply the silicone caulk, tub-n-tile sealer let it set then remove the weight. Otherwise you’ll be right back it the same shape it’ll just take a little longer. This is the same method used when applying tub-n-tile sealer around a bath tub. You fill the tub with water before you apply the sealer / caulk. Otherwise it will also pull away over time.
