I agree with imafan about the basil needing more oxygen; in fact, I think
most plants need more oxygen than provided in the Kratky method, which is why I am not a fan of it. I grow basil from cuttings all the time in deepwater hydroponics, with not only an airstone in each tub, but a small powerhead, with a sponge attached. And when rooting cuttings, I dip them in an H2O2 solution initally, to sterilize them, before rooting. Sometimes, when rooting a lot of cuttings, I do it in a cloner, but when doing just a couple, I do it in the DW, just dunking the cutting in rooting gel, then put it in the basket, with ceramic pellets around it, and it roots fast. Here's a good example, showing a bunch of basil started from cuttings, compared to a couple started from seeds the same day. The epazote grew even faster!
Hydroponics, 10-11 by
pepperhead212, on Flickr
And here's what the roots should look like, on the basil:
The roots of one of the basil plants in the hydroponics. by
pepperhead212, on Flickr