Why do some insects become motionless when a predator attacks?

Answer: Their stillness can make a predator stop attacking them

They must cool their muscles before they can flee — Cooling the muscles is not the mechanism that makes playing dead useful. The benefit depends on how the predator responds to motionless prey. The insect may resume movement after the immediate threat passes.

Their stillness can make a predator stop attacking them ✓ — Remaining motionless can interrupt an attack by a predator that responds to movement or loses interest in unresponsive prey. This defensive response is often called playing dead or tonic immobility. It works against some predators, not all of them.

They enter ordinary sleep to recover from the encounter — This sudden immobility during an attack is a defensive response, not ordinary sleep. By stopping movement, the insect may reduce further attacks and gain a chance to survive.