The kinetic energy is not conserved throughout the process like the momentum, but it is the same at t=-infinity and t=infinity if the two particles are not interacting at those "moments" (i.e. long before and long after the collision).
The total energy is conserved throughout the collision, though.
In between the end points (but most especially right around the collision) the kinetic energy is transferred the the repulsive field pushing the atoms apart. This field momentarily stores the energy and then by pushing on the atoms, the energy is delivered back as kinetic again.
This is also what happens in a mass-spring oscillator.