This happens to me all the time while listening to the radio while driving.. Wish my car radio had a skip back button.
XM. (Ok, SiriusXM) My radio does just that, and even if you change channels, it will playback whatever you were listening to for something like an hour back. My radio also can record up to 10 songs, and alert me to an artist playing or song playing on any XM channel. I spend a fair amount of time in the car and all that is worth the subscription. The decades channels and MLB are alone worth it for me.
I'm told they intend to add the feature they recently added to online listening. Even if you come in part way to a song, you can go back to the beginning of it. Supposedly you will be able to enable this for a set amount of channels. I'm guessing the radio will be able to monitor a set amount of time to some channels you are not listening to, and when you change to it you can go back that set amount of time.