I love the Yahoo News Digest app for iPhone, but hate how it kills my battery life (as of app version 1.1, February 24, 2014). Turning off Background App Refresh seemed to help a little, but only made a marginal difference.
If you want to use the Yahoo News Digest app without draining your battery, you’ll have to manually force the app to close when you’re done using it. Just double-click the Home button, find the Yahoo News Digest app, and swipe up.