This is one of the things I have been doing and I think it works well (hope it helps)
For every feedback, regardless of how small it is, I replied to the user - thanking them and asking them further questions.
For example, someone sent an email correcting me of a typo on my website. I fixed it and though I could easily NOT reply, I did and asked further questions about the site.
If getting feedback is important, I think responding to them is just as important and I don't mean responses like "thanks for your feedback", but responses that are going to proactively help you to get further feedback.
For me, this approach has had the following implications
- If it's a bug, it has forced me to attend to it immediately however small the bug is. So that I can quickly respond to the user. If you are not even fixing the bug immediately, shouldn't you question your motivation for your startup?
- It gives you an incredible opportunity to build relationship with your users. When I receive feedback from users (my target audience is developers), I usually offer feedback in return since many of them will have projects on their own. And this allows a number of emails to be exchanged.
- If you use Gmail, some of your users will appear with their social media profiles (or tools like Rapportive) - this will start you easily on doing some background survey on what kind of users they are.
- Sometimes I used this approach to ask direct questions - such as "Do you think you'll pay for this service?" or "Could you please write about my site on your blog?". Never hurts to ask (and ask nicely of course).
Hope that helps.