For me, I suppose the actual question is How would you freshen your shop if you could manage to get your act together and find some time... Febreze never seems to work.
Lately, the being a musician part of my life has been taking up most of my time, but when I'm managing to keep up, here's what I do.
First, I've noticed that the best thing to do is MAKE NEW STUFF! New stuff in the shop seems to garner the most new interest, which makes sense. I'm sad that I haven't made any new stuff in weeks, but see above, re music taking over. (Not a bad thing, by the way. My choir went from 43 singers to 60 singers this season - holy cow! And I've added several new private students - yay!)
Another option is to renew items to put them at the top of the search. However, with etsy starting to move to a relevancy-based search engine, this method may become obsolete. To which I say, it's about time!
One other great, and relatively new, etsy feature is the ability to rearrange the shop. Now that we can drag and drop items, it's much easier to change up the shop's appearance without having to spend relisting fees.
I like to arrange my shop in rows of similar items to give it a bit of organization, like this.
To read more EART answers to this question, check out the EART blog.