I would actually say that 'now' if fixed in a given reference frame. The problem is then that each person will evolve in a different frame, and the way different frames are related to each other mixes time and space (so that we loose the notion of now, in some sense).
not just evolve in a different frame but move between them, so even as a person evolves the now they had before even looses meaning. But I do see your point.
"Moving" between frames does not mean much. You can transform what is happening in a given frame (your rest frame for instance) to another one (my restframe for instance), and assuming we move fast enough, time and space are mixed and we loose the notion. This was actually what I tried to say :p