How does the current remain the same in a circuit?

The charges obviously lose energy in the lamp and so become SLOWER

The charges lose potential energy, not kinetic energy. Since they're not slowing down, it's not a problem.

Imagine that I let my car drift down a mountain. The engine isn't running, but I'm in control with the brake pedal. And I'm going to make sure the car always moves at exactly 15 mph.

The car starts with some energy at the top of the mountain. As it moves, it pushes energy into the brakes. Why doesn't the car slow down? Because it's gaining exactly the same amount of energy by dropping down the mountain. The speed and kinetic energy don't change because the energy sent into the brakes is identical to the change in potential energy by moving lower down the mountain. Or you could say the force from the brakes is balanced by the force from gravity.

If the slope is steep, I press harder on the brakes and they get hotter. If the slope is gentle, I release the brakes and they cool off a bit.

In the circuit, when the charges move through the resistor, the energy lost to the resistor is balanced by the energy from the electric field. The resistor is trying to slow down the charge, but the field in the resistor is pushing them along so they keep their speed.

At the "end" of the circuit, the charges have minimal potential energy (like the car at the bottom of the mountain). The voltage source does work on the charges and moves them to the part of the circuit with the greatest potential energy.

The circuit in its whole will settle into an equilibrium state. If you were to shoot a very short pulse of electrons through your lamp, then indeed, the current would decrease right after the lamp.

But if you have a constant flow, then, as another user illustrated, you'd have electrons bunch up right before the lamp, which limits the output, but ALSO the input! The "traffic jam" works its way backwards, all the way to the source, and eventually slows down all electrons from source to lamp.

The question

The charges obviously lose energy in the lamp and so become SLOWER, which should mean current decreases, right?

shows that you have a misconception about the motion of the conduction electrons.

If you were correct then to maintain the same current around a circuit by a miracle more conduction electrons would need to contribute to the conduction process as you went around the circuit.
If this did not happen then the conduction electrons would move slower and slower and . . . . . eventually stop?

In fact what happens is that the electrons gain kinetic energy (and lose electric potential energy) between collision with the lattice (bound) ions from the electric field in the wire and then lose that extra kinetic energy to the lattice ions upon collision with them.
The net effect is that the temperature of the material increases as the internal kinetic energy of the material has increased (the lattice ions vibrate more) and the conduction electrons move along the conductor with a constant average speed.