It's actually less about the engines and more about the wings. As altitude increases, the air becomes thinner. That means that wings stall speed increases. At the same time, as the air becomes thinner, the speed of sound decreases - and breaking the sound barrier will break your plane. As you go higher, the stall speed and the speed of sound converge.

The point where they meet is called "coffin corner". It is really not a nice place to be: If you are in coffin corner, if you try to descend, you risk speeding up and breaking the plane. If you try to slow down, you risk stalling - although it is possible to recover from a stall, you cannot recover without speeding up.

It is generally advisable stop climbing before you box yourself in like that.