The Chrome app should include both https and http in the manifest's 'urls' value
The Chrome app currently only has "http://app.mystudylife.com" as a URL for the app. This means that as soon as the app redirects to the https site, the Chrome taskbar no longer considers the app as being launched.
The example manifest at https://developers.google.com/chrome/apps/docs/developers_guide uses a wildcard in place of 'http' in the app URLs field, which is probably what MyStudyLife should be doing as well.
Updated in Chrome Web Store, thanks for the tip! :)