I had an impression that Arduino Due has 96KB of memory and an array of this size should not be a problem.
Seems right to me.
Am I doing something wrong?
Well, you didn't post all of your code.
How can I get that large array to work?
You need to define what doesn't work.
Global arrays are initialized to 0 by default. So, supplying an initializer to initialize one element of the array to the default value doesn't seem useful.
It might be, and I'm just guessing here, that the compiler doesn't properly initialize arrays that large. You could put a for loop in setup() to initialize it.