How to improve response time of this sound operated LED?
I think the problem is in the times you check the sensor. If you clap exactly when you check it will glow even if clapped for 1 ms, but if it checks in between two claps it doesn't detect it.

So check more often (reduce the delays) and check for so many sound detections within one second.

Or, as JRE below proposes, use an interrupt, this is even better but needs a bit more programming skills. Still interrupts are used a lot in microcontroller programming so it is worthwhile to check into this.