Explain why the top of an energy pyramid does not have an arrow showing energy going back down to the bottom.

The answer to your question is that all of the energy is ultimately radiated into empty outer space as heat. The second law of thermodynamics mandates that all processes that involve the transfer of energy MUST radiate a portion of this energy into space as waste heat. This is why when you run down the street you get hot and sweaty, and this is why automobiles MUST have a functioning radiator and nuclear power stations MUST have evaporation cooling towers or else be located near a large body of water to exchange excess waste heat into, etc., etc. It is also true that the transfer of energy at each step up the food chain is very inefficient. They say it takes around 50 lbs of corn to produce one pound of beef, and it probably takes 20-30 pounds of beef to produce one pound of human tissue. The rest of the energy just goes into your living room as radiated body heat. I hope this helps.

Energy does not go back to the bottom of the pyramid. Energy is used by the organisms in that level or passed on to decomposers when the animals die. Some of the energy is lost to the atmosphere as heat from the animal's body.