I do not think the solution stays at 125 ppm N Intruder, as the plant is extracting nutrients from the solution (and increasing that of the waste products). Concerning the gradient issue, consider this:
If anything, the nutrient concentration would be greater not at the bottom, but higher in the medium, as that is where the majority of the evaporation occurs. (Proof for that is the fact that the top surface is where we see the precipitation of minerals.)
However, were are talking about a pretty dilute solution to start with, and nature abhors gradients, so as the water evaporates, the solution will try to stay uniform throughout.
All in all, the nutrient concentration is probably less of a concern that the build-up of waste products.
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