This could be a few things:
Are you fertilizing? Excessive nutrients can cause knock out roses to have brown leaves. It's basically salt damage if that is the problem, water without fertilizer for a while, you can try top dressing with compost next year for a slow, light release of nutrients. 
It could be a fungal disease as well. When did you start seeing this? I would imagine you would see that in cooler weather, which we don't have right now! If it started when it was cooler out, you may try just watering the soil and not wetting leaves. 
The way they are browning from the outside looks a bit like leaf scorch. Do they get any shade? Protection from the sun and maybe a little more irrigation during the hot months could help if this is the issue.