Sometimes I do remix old projects, usually right after learning some new technique or acquiring a new plugin. Starting with an existing project lets you dive right in to the mixing process.
As Karyn cautions, sometimes I merely fall into the same mistakes the second time around. However, most of the time I manage to improve on the original mix, sometimes dramatically. I've even salvaged a couple long-discarded "failed" projects.
You don't necessarily need new monitors to hear things differently. Your ears are getting trained every day whether you're consciously aware of it or not. You'll therefore hear subtleties today that you didn't hear a few years ago.