Having fun while being accurate!
udvat, we're still missing information as to the concrete context of the question. What or why are you saying that something is becoming unbounded?
Your gradient's value, z, is determined by your function f(x,y). Likely, your function works correctly over a finite, defined x-y plane, such that all z-values are bounded within that plane, meaning they do not exceed a certain value, M. Once you go beyond that plane, your function is unbounded, ie. it doesn't constrain itself to be below some M.