There are a number of things you can do to increase your downloads -

First there is the generic things, like stand out icon for the app store, and feature rich description (its important to note apps are like websites seo is important to get people to find your app), make sure you have a working app - check error reports and fix them - your app must be built in a way that users should have no reason to delete it.

It sounds like you already have a popular website with strong traffic, your main goal should be to convert that traffic into app users. Either through advertising the app via your website, or you can even use one of those plugins that detect if the user if looking at your site via their mobile phone, and automatically suggesting they use the app instead.

There are literally hundreds of thousands apps out there now, so to make yours get the users and keep them you have to work hard to keep the users you get - if you acquire 500 users in a month but lose 300, its going to take a very long time - use analytics to see exactly where you are losing customers and fix it, ever user is important.