Why is more difficult to push a stalled car from rest than to keep it in motion once it has started to run?

Inertia.

When you first start to push the vehicle you need to overcome the inertis of the vehicle and provide it with Kinetic energy.

Once the vehicle is moving, i.e has kinetic energy, then to keep a constant speed on a level surface you only need to push to replace the energy lost through friction, drag, and other energy losses