Explanation for behavior of acetic acid in aquaponic/hydroponic systems? Because aquaponics is hydroponics with fish &amp; bacteria, options for adjusting pH are limited.

Primarily people use phosphoric acid, hydrochloric acid, and nitric acid (heavily diluted).  A less popular but easy to acquire material is vinegar.

I've tried using it in a very alkaline solution (100 ppm calcium carbonates, 8.4 pH) and noticed that the pH would drop by a small amount before returning to it's original state.  Anecdotally, other aquaponic hobbyists have noticed a similar effect that is not replicated by the other acids. What is happening that the pH would lower temporarily and then rise back up over several hours?
The source of the acid shouldn't matter much in adjusting the pH by a small amount.  What is the source of the calcium carbonate?  

If it is dissolved calcium carbonate only, as you might find in hard water, then this is strange.  The solution is buffered by the combination of dissolved carbon dioxide and carbonate minerals, so its pH might be difficult to change, but once it has been changed it should stay where you put it, more or less. 

If you have solid calcium carbonate (cement, limestone gravel, some pottery (notably not terracotta) or marble chips, perhaps), then what is happening makes a lot more sense.  You add acetic acid, lowering the pH and consuming some of the carbonate from the solution.  There is a large reservoir of carbonate available though, in the form of the carbonate minerals, and that eventually redissolves and the solution becomes more basic with time.