They usually only release a certain number of seats for rewards. These are not on every flight or even on every day. So if you can’t get exactly what you want, you probably need to consider taking award seats on dates that are available or paying for a seat. It’s possible, but, in my experience, unusual that they may add a few extra seats closer to departure. Say if someone cancels an award booking - although it seems that theses seats may also be returned to the revenue sale pool.
In short, I’d say if you see something suitable even if not exactly what you want, book it before it vanishes.