Also please note, the P chanel has a threshold voltage of zero because its "ideal" for the sim.
So there is not much chance of the mosfet turning off!
Once the voltage on the load has dropped below the forward voltage of the LED (1.2V ?) there is no load on the circuit. Any leakage - no matter how small - must go through the base of the transistor Q3 - which in turn is amplified and pulls the gate of the mosfet further away from its off-state.
How is it possible to work in the video and not in the sim. Its clearly set up the exact same way
As you have discovered, because it requires mammoth amounts of computing power to make a completely accurate simulation, some corners are cut and some "ideal" components or conditions are assumed.
When you transfer this simulation to real components there will be other traps revealed by the non-ideal components, e.g. does the simulation account for button-bounce?
Edit: Just noticed that R3 and the base of Q2 will allow take some current away - but only until the voltage drops to 0.6-0.7V - still enough to start Q3.
Another thought on simulation: If your are having problems with a simulation, break it down into small chunks and simulate these in isolation. Build the simulation from small bits that work and, importantly, you understand how they work.