Draft hooves do tend to break off in chunks. More to do with their origins in wet europe as opposed to dry asian climates. Nothing you are doing wrong. Just the way it is. You are doing a good job and your horses look lovely. Don't worry so much.
Get your farrier to show you how to touch things up between appointments. When I had mine I actually had to have my husband work the nippers in the summer. My hands just weren't big enough to get a decent grip to get through hardened wall. I could do the rest myself. Just took longer but I'm slow anyway and the horses sometimes get impatient with me.
There are a lot of pictures of the internal structures of the hoof, draft next to light horse horse here:
WHAT IS A HEALTHY HOOF AND WHAT DOES IT LOOK LIKE
Little warning...several of dissected cadaver feet so if you are squeamish be warned. Many pictures and most aren't icky.