Laser Turrets and Point Defense Batteries are able to do Point Defence. Point Defense Batteries take up 20 dtons of space and a lot of power because they have their own built in computer systems for automating fire control. Turrets need someone (a virtual gunner or real gunner) controlling them to take the Point Defence reaction. PD Software is entirely unrelated to taking a PD reaction.
That reaction can only target missiles coming at your ship. The range *to* the missile is not relevant.
The relevant rule is:
Point Defence may only be performed against missile salvos (see page 172) as they are about to make their attack roll against a target – missiles are too small and too fast to be targeted at greater ranges.
The range at which missiles are "about to make their attack roll against a target" is Medium. Once a missile is in medium range, it is hitting that turn.
What Point Defence Software does is allow any Point Defence weapon (turret or battery) to defend another ship against missiles fired at that other ship. It has no effect at all on missiles fired at your ship. The ranges (Close or Short) is the distance between your ship and the ship you want to defend. Not the distance to the missiles.
The Imperial Close Escort Notonmywatch is protecting a trio of fat traders from missile attacks by a pirate fleet. The Pirates are at Long Range. They launch missiles. So there is 1 turn where the missiles approach and then on the second turn, the missiles hit.
MV Just Another Rustbucket is staying Close to Notonmywatch. MV Party Girl is a bit further away, at Short Range. MV Doing My Own Thing is making a run for it and is now at Medium range from Notonmywatch, which still leaves it within Long Range of the Pirates.
The round the missiles are launched and the round they are going to hit, those missile salvos are subject to Electronic Warfare if there is someone taking the Sensor Ops role on the ship. The Sensor Ops on Notonmywatch can make EW actions against missiles aimed at their their own ship and Just Another Rustbucket because that ship is in Close Range. So, assuming two crewed sensor stations, the missile salvos aimed at Notonmywatch & Rustbucket will endure two EW attempts (one each per turn of missile travel time). Rustbucket, even if it had sensor ops, can't do anything more because only 1 EW per salvo per turn and Notonmywatch is doing that for the missiles aimed at it. The other two merchant ships probably don't have anyone one Sensor Ops duty, so missiles aimed at them probably don't have any effective EW directed their way. But if they did, the EW attempt is at -2 because of the lousy sensor suites on merchant ships.
On that second turn, all four missile salvos are going to hit with whatever survived the two EW attempts. If Notonmywatch does not have any PD software, it is every ship for itself. The escort can only defend itself and each merchant has to try to defend itself with any manned laser turrets it has.
With PD Software 1, Notonmywatch can split its PD between its own defence and the defence of Rustbucket, because Rustbucket is within Close range of Notonmywatch. If Notonmywatch has PD Software 2 running, it can allocate its PD to the salvoes against itself, Rustbucket, or Party Girl because Party Girl is within short range. At no point can Notonmywatch do anything to protect Doing My Own Thing, because it is at Medium range from Notonmywatch.
So, each of the merchant ships will fire any manned laser turrets at the missiles coming at their own ship. Notonmywatch will divide its options amongst whichever ships its level of PD software allows it to cover.