There's currently a shortage of pilots on BA's 320 fleet. Consequently, there appears no reason why the FPP wouldn't run for at least the next two or three years. Furthermore, if the rumours are true that BA haven't been able to acquire the numbers they wanted on this intake (and indeed on previous intakes) then they may well choose to run the FPP even longer to cover the shortfall. Nothing is guaranteed though.
If previous FPPs are anything to go by then it'll open up for applications again around November.