Why Google Play Music app gets turned off when I'm running? Whenever I go for a run and I'm using my Google Play Music app, my phone turns off within 5-10 minutes, causing said app to turn off.  

Is there a way to stop this from happening?

If relevant I have a Samsung Galaxy S III.
Check your settings within Google Play Music for 'Stream via WiFi Only'. If you have this set, and you're out of range, the streaming cannot continue until you return within range. It may just be coincidental to always appear consistently at that time or range.Also remember about caching. Caching may queue a number of songs, making it appear to extend range.