I hope I haven't written something too foolish. The half life should be constant but I'm not sure I can argue it in a qualitative manner. Maybe you could view it as a gemetric concept. You have a segment in the plane and each second you cut off a certain percentage (i.e. a certain percentage of the nucleuses decay), this is something "geometric" and shouldn't depend on the coordinate system, and thus not on the length of the segment. So no matter the initial length (or number of nucleuses) you'll end up with the same number of seconds to remove half the segment.