I also had this problem.

It seems like the stock internet radio player has a problem in that when it most begin buffering while playing, it turns off.

This was a problem for me especially because I wanted to use it with Alarmed as a clock radio alarm.

My solution was to download KMPlayer, which I now use as the application to play internet radio stations called by Alarmed when I set it to wake me up. KMPlayer does not have the problem with shutting off, it just buffers & continues.

I found no solution to the problem with the stock internet radio player.