In August 2011, Etsy changed the search default from recency to relevancy. Prior to that, renewing was a way to get more views. Now with relevancy, working on titles, tags, descriptions etc. increases opportunities for views.
However, when you go to the front page and use Categories to search, that is defaulted to Recent unless you click on Relevancy. Also, at the bottom of the page, recently listed items scroll. I do notice a renewed item is more popular the day it is renewed, but not for long.
Check your shop stats and see if you get more views from Search or Categories. I get more views from Search, so I focus on relevancy rather than recency and renewing items only when they expire.
I hope this makes sense.