1. What does “order greater than 3” imply?
   A reaction of order $>3$ would typically require an elementary step involving the simultaneous participation of many reacting particles.

2. Why are such reactions rare?
   For an elementary reaction to occur in one step, the required molecules must:

   • collide simultaneously,
   • with proper orientation, and
   • with sufficient energy.

   As the number of molecules involved increases, the chance that all of them collide at the same instant with the correct conditions becomes extremely small.

3. Evaluate the options:

   • A: increase in entropy and activation energy as more molecules are involved
     Not the standard reason. The rarity is mainly due to collision probability, not stated generally in terms of entropy and activation energy.

   • B: shifting of equilibrium towards reactants due to elastic collisions
     Incorrect. Elastic collisions do not explain why higher molecularity reactions are rare.

   • C: loss of active species on collision
     Incorrect. This is not the fundamental reason.

   • D: low probability of simultaneous collision of all the reacting species
     Correct. This is the accepted explanation.

4. Conclusion
   Higher order reactions are rare because the probability of simultaneous effective collision among many reacting species is very low.

Therefore, the correct option is: $\boxed{\text{D}}$