The "Are you still listening?" message comes up when we detect that you have not interacted with the player for a while. This is in place to avoid the cost of streaming music into empty rooms. For example, some people may start playing Pandora at work and leave it running after going home for the day. Since we pay full royalties on every song we play, having a timeout interval will enable us to stop from streaming endlessly to unattended devices. It helps us keep Pandora free for everyone.
All you need to do is click (or tap) somewhere on the Pandora music player once in the time-out period, and you should not see that message.
Also, if you upgrade to Pandora One, which will remove all ads from the site (among other things), the time-out will increase. We recommend upgrading if you'd really like to listen for long periods of time without interacting with the tuner. You can find information on Pandora One here.