The question essentially is asking that if a given system started in one state then went through a series of changes and eventually came back to its original state, then how would it be possible to measure time??? To elaborate, if the universe were to eventually revert to conditions before the big bang /inflation start, then it would be impossible to differentiate between the start of one "time" and the start of another "time". Whatever your definition of time is, it is intrinsically linked to the measurement of change, so if your system changes so much that it returns to its original unchanged state, then the notion of time is irrelevant. one time would be identical to another, with all the time inbetween simply an indicator of stages of change.
Any clearer?
DG