To be clear, if I can’t find availabilty on BA.com, I check on Asia Miles. Ba.com frequently blanks CX availability online particularly at later availability because of apparent Avios fraud occurring.
If you find availability on Asia Miles, then you’ll need to call up BAEC to book, and for them to manually check availability that’s not showing on BA.com. I’ve always found Asia Miles availability means there is Avios availability, and if it doesn’t show online on BA.com, I can book over the phone through BAEC.
Others have described different experiences, with Asia Miles availability apparently not always equating to BAEC Avios availability even when calling up. Perhaps I have been lucky, but I’ve booked dozens of Avios redemptions on CX and always found the Asia Miles availability to match BAEC’s once I call BAEC up.