Check the basil leaves for any discolouration. Also, when you take it out of the container, check to see if there are any little whitish blob things on the root hairs. If there are, KEEP them on. Those whitish blob things are fungi, which are in a symbiotic relationship with the plant, known as mycorrhizae. If you didn't understand the last sentence, consider this example:
Plant A has normal roots, healthy soil, etc...
Plant B has normal roots with mycorrhizae, healthy soil, etc...
Both will grow, however, with the mycorrhizae, it'll grow larger. Fungi are great at absorption, thus they give the plant more water and nutrients. In return, fungi are non-photosynthetic but plants are photosynthetic, thus they provide fungi nutrients and avoid it dehydrating (possible from high ratio of surface area : volume).
Reading back on this, I sound nerdish...