Young stellar objects often drive powerful bipolar outflows, which evolve on timescales of a few years. An increasing number of these outflows has been detected in X-rays implying the existence of million degree plasma almost co-spatial with the lower temperature gas observed in the optical and near-infrared. The details of the heating and cooling processes of the X-ray emitting part of these so-called Herbig-Haro objects are still ambiguous, e. g., whether the cooling is dominated by expansion, radiation, or thermal conduction. We present a second epoch Chandra observation of the first X-ray detected Herbig-Haro object (HH 2) and derive the proper-motion of the X-ray emitting plasma and its cooling history. We argue that the most likely explanation for the constancy of the X-ray luminosity, the alignment with the optical emission and the proper-motion is that the cooling is dominated by radiative losses leading to cooling times exceeding a decade. We explain that a strong shock caused by fast material ramming into slower gas in front of it about ten years ago can explain the X-ray emission while being compatible with the available multi-wavelength data of HH 2.