Some posters here have the broader experience that BA does have awards on CX. Regional J awards are not too difficult to find. Longhaul J awards are hard to find while Y is easier.
All airlines now have sophisticated yield management IT, including for awards. CX gives priority to its own FFP. It is not unusual that a CX award is open for some time only to AM, especially for DMs, then finally open to partners if they are not taken. As mentioned above, CX tends to release more awards a few days before departure if the load is light.

Just looking at one month can be misleading. For example, February is Chinese New Year travel season. It could be that CX basically releases few, if any, awards to partners.