WSJ attribute the decline of Big Band music to a tax.
Wikipedia attributes it to:
a loss of quality (due to WWII deaths of key members) and
a 1942 musician’s strike (causing vocalists to break away from the bands, leading to an emphasis on the vocalists) and
changing tastes to non-danceable music (bebop, cuban, modern jazz)
http://en.wikipedia.org/wiki/194244_musicians’_strike
There was also the small problem that ascap and BMI would not allow musicians to record their music....
ha ha ha ha