Maybe before someone tries to leave your app, you 'pop up' a survey asking how they liked it. Get them to add their own answers so you can hear more how they feel about your app and see what's bothering them.

There are plenty of people on youtube that review products, one comes to mind is iJustine. I know she accepts requests and she has a very large following. Send her a request and maybe she can do your app some justice.

Post videos to youtube as well to promote the app from twitter. Is it on facebook? Vimeo?