I've been using Avios for several years to book CX regional flights in J/F. Availability used to be excellent. Within the past year or so, it's decreased dramatically. Though I agree with the comment upthread that space will often open 2 or 3 weeks prior to departure.
I now find SQ KF much better for Asia regional flights, though it tends to be a little more expensive than redeeming Avios. Obviously less useful if you're based in HKG.
I also seem to recall reading that CX availability may differ based on which website you're using . . . if based in HKG, you may be seeing lesser availability than if you use the UK or US website.