Well I'm not an expert, but I have some experience with horses and I have read lots of cavalry books...
I would think a broken down horse in this context would be...
1. "Galled up" i.e. sores where saddle has rubbed it raw, prevents horse from being ridden
2. Thrown a shoe or two no replacements to be had.
3. Exhausted or "played out" and unable to be prodded to move.
4. And the more obvious onset of lameness, sore/inflamed tendons, etc
Most of the time a little R&R plus veterinary attention will resolve most issues. Of course this would not be practicable on a raid and those horse would be culled.