How do you keep knock down texture from peeling off with paint application?

Use "all purpose" compound for the texture. It will be a little stronger than topping compound. You could also use "Hot mud", which is a LOT stronger and won't soften when it gets wet. Part of your problem is, you're using a water based primer or paint over the texture, then you're rolling it. Try either using an oil based primer or just spray the primer over the texture without using the roller. Once the PVA primer sets up the texture should be strong enough to take the finish coat without trouble.