As suggested in this thread.
Concelhaut's Draining Touch has a casting time of 3.0s / 4.0s, which compares rather unfavorably to that of other summoned weapons (consistently at 3.0s / 0.0s).
Considering that, contrary to other summoned weapons, Concelhaut's Draining Touch disappears after hitting your foe once*, I see no reason for its casting time to be any longer.
* The thread also mentions that Concelhaut's Draining Touch will not disappear if used in a Full Attack with another we