There are a set number of Avios seats made available on all BA flights as they're released for sale (355 days before), however these can get booked quickly (on some popular routes and/or dates you have to book on the dot at midnight). Once the initial tranche have been booked there is a chance that more Avios seats will be made available, but there's certainly no guarantee of this.

A flight being available for a cash booking has little relevance to Avios seats being available unfortunately.