Ah, it seems my question has uncovered a false assumption you have made by comparison of a similar method of growing.

In hydroponics, you have to change the water because of several reasons, but 1 being coincidentally the same as what I listed above earlier. The SALTS build up that make up the INORGANIC nutrient solution filled with dissolved solids you use to feed the plants. As these salts reach fatal levels, the plants are unable to take up water or nutrients and DIE. So, the only solution is to change the water.

In aquaponics, the nutrients are mainly derived from the processed waste of the fish by microorganisms. The nutrients, although water soluble, are not SALTS, but rather ions that get eaten up by the plants. When nutrients are provided in an ORGANIC form they are readily broken down in organic systems and therefore do not cause fatal buildups if balanced. It's all more complicated than this, but remember, it's a miniature ecosystem you are building! The cycle is self-contained; therefore, you do not have to waste water like that (and in fact is one of the main reasons behind why aquaponics was researched at the University of The Virgin Islands and why it has been so successful in Australia).

With that said, you should watch your levels. If your levels are out of whack such as nitrate, you will want to change out some water. This water can be used to fertilize soil plants or in pure hydroponic systems where relatively high levels of nitrate for fish are inconsequential to the plants. My first aquaponic setup was a 10 gallon tank. I must have spiked the nitrate up to 800ppm at one point. I lost 1 fish of 35; afterward, I used most of the water in a hydroponic DWC bubbler system. The plants did great, and the remaining fish thanked me for it! LOL