Extreme close range is the key, but it works not because of time limit but more of the radar blind area created due to the close range. APS simply can not see the incoming projectile. For reference, China's GL-5 is stated to be able to intercept the projectile at 1.5 meters and beyond provided it can be seen by the radar, the time it takes from detection to destruction is in the milliseconds.
There are four radar panels. In the horizontal plane, if each one covers 90 degrees, it can cover 360 degrees without blind area ONLY if the panels are mounted right next to each other. In reality they are mounted on the four corners more than 2 meters apart. This create a infinite gap. To cover the gap each panel need to cover more than 90 degrees to overlap, the more the better, but there is always a blind region. It is illustrated in this diagram. The green area is the blind region, it is more than twice the width of the tank or 8 meters of Merkava.
View attachment 123201
In the vertical plane, the covering angle is much smaller giving a much longer blind region especially downwards because panels are mounted more upwards. Assuming the downwards angle is 8 degrees and the mounting point is 2 meters, the blind range extends to 14 meters of Merkava.
I took the radar covering angle figure from China's GL-5. Since there is nothing secret in case of design principle, capability, limitations of AESA radar, I think it is accurate enough for illustration purpose.
I recall Trophy system's interceptor launcher has to flip up and pivot towards the incoming direction. At such close range I can see why the system does not have enough time to respond.
For such short distances it is probably better if interceptor launchers are installed in fixed angle and just launch in the general direction without pivoting.