I called the office two or three times, but _______ time no one responded.

'Each' is used to refer to every individual member of a group considered separately. The sentence indicates that on every single occasion of calling, no one responded. 'Each time' emphasizes the individual instances of calling. 'All time' is ungrammatical here, 'some time' would not fit the negative context, and 'any time' doesn't fit the structure. Therefore, 'each' is the correct determiner.