I am running an HO scale train on 46 feet of EZ track.  I have a new transformer that generates plenty of power.  At one point the train hesitates, the lights dim, and then things go back.  It is NOT a dirty track.  I have cleaned the track, I have replaced twelve feet of track in that section, and it still hesitates.  What is the problem and how can I fix it?  Everything is less than 90 days old.

EDIT: This is not at the "halfway" point from the power source.  It is about 3/4 of the way through it, i.e. ~12 feet from the power source on one side and 34 feet on the other end.