I always ask for feedback (I have another Etsy shop as well), but do so in my "thanks for ordering" email. But make sure you slant it as a positive to the customer... something to the effect of, "I would appreciate you leaving positive feedback for me on Etsy. If for any reason you wouldn't leave positive feedback, please let me know what I can do to fix the situation." I once had a customer reply and say, "You know, it wasn't a big deal, and I wasn't going to say anything, but <issue>." I fixed it; she left glowing feedback, AND gave me referral business.
That being said, I would never email/convo someone to ONLY ask for feedback. I only incorporate it into conversations and it's proven beneficial to me.