We've been on Etsy for just over 4 years now (if I remember right) with http://www.shireeodiz.com
and as several of you have mentioned, it's not as easy as just posting great products and great content. Although they would probably like to distance themselves from eBay and Amazon, Etsy have one major common denominator - a search and discovery algorithm. Without learning the basics of how their algorithm works, you will be forever fighting for traffic. Even when you do know how the game works, it's still not easy.
Some of the basics for getting exposure with Etsy SEO are:
1. Keep customers happy and get good ratings
2. Ship on time (preferably with tracking) and update your Etsy account - late shipments are starting to affect search rankings.
3. Use product variations on a single listing to attract more buyers to one page
4. Sales history counts so be attractive with price and promote your best sellers first (Etsy doesn't want to 'waste' their traffic on dud listings). Remember that Etsy makes more money from listings that sell - they're happy, the buyers are happy and good sellers are happy when the most sellable listings are higher up in search.
5. Remember to use keyword rich titles and tags
6. Build reputation and sales history by getting traffic from external sources (social media, newsletters, blogs, etc)
7. Use promoted listings on Etsy to keep your best sellers selling
8. Regularly post new items for fresh traffic
9. Create new listings for old listings that didn't sell, rather than relisting them. This tells Etsy that it's a new item (perhaps worth promoting) rather than the old one that they know didn't sell. Relisting is okay a few times, but once stale, make a change.