Charged capacitor doesn't allow impulses to pass
Initially, the voltage on the + plate of the capacitor is 0V.

Pressing S1 connects it to a 9V source; current flows, charging the capacitor.

On releasing S1, the voltage on the + plate of the capacitor remains at 9V.

Pressing S1 again connects a 9V source to a plate charged to a potential of 9V, so no current flows. The LED does not light again.

If you attach a highish value resistor (10k-100k) between the + plate and ground, it will discharge the capacitor between presses of S1, so it will light again for each press of S1.