I've created an "Apps for Office" mail app that's working in both the Outlook 2013 desktop app and Office 365 on desktop browsers. However, when I use Office 365 on a mobile browser the "app bar" never loads and therefore there's no way to launch my app. I've taken a desktop browser where my mail app appeared, switched the user-agent to a mobile browser agent, and the app stops loading.
According to Overview of apps for Office:
Apps can run in multiple environments, including Office desktop applications, Office Online in both desktop and mobile browsers (my emphasis), and a growing number of Office tablet and phone apps.
What am I missing?
Set up a mail app for Outlook on desktops, tablets and mobile devices explains what to do. Basically if you manually edit your manifest xml file you'll see a <DesktopSettings> element defined.
You can add additional <TabletSettings> and <PhoneSettings> elements to handle those cases, optionally providing entirely different pages for your app.