It is the “deemed” date of delivery that counts. If the alleged contravention was on 1st August and the NtK was “issued” on Monday 11th August, then the deemed date of delivery is Wednesday 13th August, which is only 12 days after the dare of the alleged contravention, and so within the relevant period as far as PoFA is concerned.
You are unlikely to win this at IAS but if you are prepared to fight it, you would put them to strict proof that they posted it on the date it was issued. They will not have evidence of posting and as the delivery is a rebuttable presumption, you could have a very strong defence point that it was never served within the relevant period and therefore they cannot rely on PoFA to transfer liability from the unknown driver to the known Keeper.
However, all that is a bit superfluous because if you do fight is all the way to a county court claim, with our defence, they will eventually discontinue anyway.
They rely on you being low-hanging fruit on the gullible tree who will, under pressure, pay up out of ignorance and fear.