Pre-COVID, there were fraud restrictions for redemption of Avios on certain routes. Absolutely no recollection of the details but a search on here (or the BA forum) might turn them up. From memory, calling BA could sometimes help get seats that weren’t visible online but I think that was only for flights a few days away.

More generally, CX offers different award availability to partners than to its own Asia Miles members. You may have found a situation where they haven’t released flights to partners or the limited seats made available have already been redeemed.