OP- have you considered that your soil may have Fusarium, which could be causing the wilt issues you're experiencing with Basil? Are you growing tomatoes in the same bed/soil? If so, are the tomatoes healthy through the entirety of your season? Here are some links (note the pic in the 2nd):
http://plantclinic.cornell.edu/facts...ildiseases.pdf
http://www.gardeningknowhow.com/edib...l-diseases.htm
Good luck (BTW, I have the same problems w/ Basil in my garden)-
-naysen